{"id":1909,"date":"2021-12-02T19:39:56","date_gmt":"2021-12-03T00:39:56","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-7-8\/"},"modified":"2022-11-02T10:38:20","modified_gmt":"2022-11-02T14:38:20","slug":"answer-key-7-8","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-7-8\/","title":{"raw":"Answer Key 7.8","rendered":"Answer Key 7.8"},"content":{"raw":"<ol>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rr}\n\\begin{array}[t]{rrrrr}\nk&amp;-&amp;7&amp;=&amp;0 \\\\\n&amp;+&amp;7&amp;&amp;+7 \\\\\n\\hline\n&amp;&amp;k&amp;=&amp;7\n\\end{array}\n&amp;\\hspace{0.25in}\n\\begin{array}[t]{rrrrr}\nk&amp;+&amp;2&amp;=&amp;0 \\\\\n&amp;-&amp;2&amp;&amp;-2 \\\\\n\\hline\n&amp;&amp;k&amp;=&amp;-2\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rr}\n\\begin{array}[t]{rrrrr}\na&amp;+&amp;4&amp;=&amp;0 \\\\\n&amp;-&amp;4&amp;&amp;-4 \\\\\n\\hline\n&amp;&amp;a&amp;=&amp;-4\n\\end{array}\n&amp;\\hspace{0.25in}\n\\begin{array}[t]{rrrrr}\na&amp;-&amp;3&amp;=&amp;0 \\\\\n&amp;+&amp;3&amp;&amp;+3 \\\\\n\\hline\n&amp;&amp;a&amp;=&amp;3\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rr}\n\\begin{array}[t]{rrrrr}\nx&amp;-&amp;1&amp;=&amp;0 \\\\\n&amp;+&amp;1&amp;&amp;+1 \\\\\n\\hline\n&amp;&amp;x&amp;=&amp;1\n\\end{array}\n&amp;\\hspace{0.25in}\n\\begin{array}[t]{rrrrr}\nx&amp;+&amp;4&amp;=&amp;0 \\\\\n&amp;-&amp;4&amp;&amp;-4 \\\\\n\\hline\n&amp;&amp;x&amp;=&amp;-4\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rr}\n\\begin{array}[t]{rrrrr}\n2x&amp;+&amp;5&amp;=&amp;0 \\\\\n&amp;-&amp;5&amp;&amp;-5 \\\\\n\\hline\n&amp;&amp;\\dfrac{2x}{2}&amp;=&amp;\\dfrac{-5}{2} \\\\ \\\\\n&amp;&amp;x&amp;=&amp;-\\dfrac{5}{2}\n\\end{array}\n&amp;\\hspace{0.25in}\n\\begin{array}[t]{rrrrr}\nx&amp;-&amp;7&amp;=&amp;0 \\\\\n&amp;+&amp;7&amp;&amp;+7 \\\\\n\\hline\n&amp;&amp;x&amp;=&amp;7\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrr}\n6(x^2-25)&amp;=&amp;0 \\\\\n6(x-5)(x+5)&amp;=&amp;0 \\\\ \\\\\nx&amp;=&amp;5 \\\\\nx&amp;=&amp;-5\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrr}\n(p+8)(p-4)&amp;=&amp;0 \\\\ \\\\\np&amp;=&amp;-8 \\\\\np&amp;=&amp;4\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrr}\n2(n^2+5n-14)&amp;=&amp;0 \\\\\n2(n+7)(n-2)&amp;=&amp;0 \\\\ \\\\\nn&amp;=&amp;-7 \\\\\nn&amp;=&amp;2\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrr}\n(m-6)(m+5)&amp;=&amp;0 \\\\ \\\\\nm&amp;=&amp;6 \\\\\nm&amp;=&amp;-5\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrr}\n(x+3)(7x+5)&amp;=&amp;0 \\\\ \\\\\nx&amp;=&amp;-3 \\\\\nx&amp;=&amp;-\\dfrac{5}{7}\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrr}\n(2b+1)(b-2)&amp;=&amp;0 \\\\ \\\\\nb&amp;=&amp;-\\dfrac{1}{2} \\\\ \\\\\nb&amp;=&amp;2\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\nx^2&amp;-&amp;4x&amp;-&amp;8&amp;=&amp;-8 \\\\\n&amp;&amp;&amp;+&amp;8&amp;&amp;+8 \\\\\n\\hline\n&amp;&amp;x^2&amp;-&amp;4x&amp;=&amp;0 \\\\\n&amp;&amp;x(x&amp;-&amp;4)&amp;=&amp;0 \\\\ \\\\\n&amp;&amp;&amp;&amp;x&amp;=&amp;0 \\\\\n&amp;&amp;&amp;&amp;x&amp;=&amp;4\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\nv^2&amp;-&amp;8v&amp;-&amp;3&amp;=&amp;-3 \\\\\n&amp;&amp;&amp;+&amp;3&amp;&amp;+3 \\\\\n\\hline\n&amp;&amp;v^2&amp;-&amp;8v&amp;=&amp;0 \\\\\n&amp;&amp;v(v&amp;-&amp;8)&amp;=&amp;0 \\\\ \\\\\n&amp;&amp;&amp;&amp;v&amp;=&amp;0 \\\\\n&amp;&amp;&amp;&amp;v&amp;=&amp;8\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrr}\n&amp;x^2&amp;-&amp;5x&amp;-&amp;1&amp;=&amp;-5 \\\\\n&amp;&amp;&amp;&amp;+&amp;5&amp;&amp;+5 \\\\\n\\hline\n&amp;x^2&amp;-&amp;5x&amp;+&amp;4&amp;=&amp;0 \\\\\n(x&amp;-&amp;4)&amp;(x&amp;-&amp;1)&amp;=&amp;0 \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;x&amp;=&amp;4 \\\\\n&amp;&amp;&amp;&amp;&amp;x&amp;=&amp;1\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrr}\n&amp;a^2&amp;-&amp;6a&amp;+&amp;6&amp;=&amp;-2 \\\\\n&amp;&amp;&amp;&amp;+&amp;2&amp;=&amp;+2 \\\\\n\\hline\n&amp;a^2&amp;-&amp;6a&amp;+&amp;8&amp;=&amp;0 \\\\\n(a&amp;-&amp;4)&amp;(a&amp;-&amp;2)&amp;=&amp;0 \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;a&amp;=&amp;4 \\\\\n&amp;&amp;&amp;&amp;&amp;a&amp;=&amp;2\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrr}\n&amp;7x^2&amp;+&amp;17x&amp;-&amp;20&amp;=&amp;-8 \\\\\n&amp;&amp;&amp;&amp;+&amp;8&amp;&amp;+8 \\\\\n\\hline\n&amp;7x^2&amp;+&amp;17x&amp;-&amp;12&amp;=&amp;0 \\\\\n(7x&amp;-&amp;4)&amp;(x&amp;+&amp;3)&amp;=&amp;0 \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;x&amp;=&amp;\\dfrac{4}{7} \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;x&amp;=&amp;-3\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrr}\n&amp;4n^2&amp;-&amp;13n&amp;+&amp;8&amp;=&amp;5 \\\\\n&amp;&amp;&amp;&amp;-&amp;5&amp;&amp;-5 \\\\\n\\hline\n&amp;4n^2&amp;-&amp;13n&amp;+&amp;3&amp;=&amp;0 \\\\\n(4n&amp;-&amp;1)&amp;(n&amp;-&amp;3)&amp;=&amp;0 \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;n&amp;=&amp;\\dfrac{1}{4} \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;n&amp;=&amp;3\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrr}\n&amp;x^2&amp;-&amp;6x&amp;&amp;&amp;=&amp;16 \\\\\n&amp;&amp;&amp;&amp;-&amp;16&amp;&amp;-16 \\\\\n\\hline\n&amp;x^2&amp;-&amp;6x&amp;-&amp;16&amp;=&amp;0 \\\\\n(x&amp;-&amp;8)&amp;(x&amp;+&amp;2)&amp;=&amp;0 \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;x&amp;=&amp;8 \\\\\n&amp;&amp;&amp;&amp;&amp;x&amp;=&amp;-2 \\\\\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrr}\n7n^2&amp;-&amp;28n&amp;=&amp;0 \\\\\n7n(n&amp;-&amp;4)&amp;=&amp;0 \\\\ \\\\\n&amp;&amp;n&amp;=&amp;0 \\\\\n&amp;&amp;n&amp;=&amp;4\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rcrrrrrrrr}\n&amp;4k^2&amp;+&amp;22k&amp;+&amp;23&amp;=&amp;6k&amp;+&amp;7 \\\\\n&amp;&amp;-&amp;6k&amp;-&amp;7&amp;&amp;-6k&amp;-&amp;7 \\\\\n\\hline\n&amp;4k^2&amp;+&amp;16k&amp;+&amp;16&amp;=&amp;0&amp;&amp; \\\\\n&amp;4(k^2&amp;+&amp;4k&amp;+&amp;4)&amp;=&amp;0&amp;&amp; \\\\\n4(k&amp;+&amp;2)&amp;(k&amp;+&amp;2)&amp;=&amp;0&amp;&amp; \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;k&amp;=&amp;-2&amp;&amp;\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrr}\n&amp;a^2&amp;+&amp;7a&amp;-&amp;9&amp;=&amp;-3&amp;+&amp;6a \\\\\n&amp;&amp;-&amp;6a&amp;+&amp;3&amp;&amp;+3&amp;-&amp;6a \\\\\n\\hline\n&amp;a^2&amp;+&amp;a&amp;-&amp;6&amp;=&amp;0&amp;&amp; \\\\\n(a&amp;+&amp;3)&amp;(a&amp;-&amp;2)&amp;=&amp;0&amp;&amp; \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;a&amp;=&amp;-3&amp;&amp; \\\\\n&amp;&amp;&amp;&amp;&amp;a&amp;=&amp;2&amp;&amp;\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrrrr}\n&amp;9x^2&amp;-&amp;46&amp;+&amp;7x&amp;=&amp;7x&amp;+&amp;8x^2&amp;+&amp;3 \\\\\n&amp;-8x^2&amp;-&amp;3&amp;-&amp;7x&amp;&amp;-7x&amp;-&amp;8x^2&amp;-&amp;3 \\\\\n\\hline\n&amp;&amp;&amp;x^2&amp;-&amp;49&amp;=&amp;0&amp;&amp;&amp;&amp; \\\\\n(x&amp;-&amp;7)&amp;(x&amp;+&amp;7)&amp;=&amp;0&amp;&amp;&amp;&amp; \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;x&amp;=&amp;7&amp;&amp;&amp;&amp; \\\\\n&amp;&amp;&amp;&amp;&amp;x&amp;=&amp;-7&amp;&amp;&amp;&amp;\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrr}\n&amp;x^2&amp;+&amp;10x&amp;+&amp;30&amp;=&amp;6 \\\\\n&amp;&amp;&amp;&amp;-&amp;6&amp;=&amp;-6 \\\\\n\\hline\n&amp;x^2&amp;+&amp;10x&amp;+&amp;24&amp;=&amp;0 \\\\\n(x&amp;+&amp;6)&amp;(x&amp;+&amp;4)&amp;=&amp;0 \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;x&amp;=&amp;-6 \\\\\n&amp;&amp;&amp;&amp;&amp;x&amp;=&amp;-4\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrr}\n&amp;40p^2&amp;+&amp;183p&amp;-&amp;168&amp;=&amp;p&amp;+&amp;5p^2 \\\\\n&amp;-5p^2&amp;-&amp;p&amp;&amp;&amp;&amp;-p&amp;-&amp;5p^2 \\\\\n\\hline\n&amp;35p^2&amp;+&amp;182p&amp;-&amp;168&amp;=&amp;0&amp;&amp; \\\\\n&amp;7(5p^2&amp;+&amp;26p&amp;-&amp;24)&amp;=&amp;0&amp;&amp; \\\\\n7(p&amp;+&amp;6)&amp;(5p&amp;-&amp;4)&amp;=&amp;0&amp;&amp; \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;p&amp;=&amp;-6&amp;&amp; \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;p&amp;=&amp;\\dfrac{4}{5}&amp;&amp;\n\\end{array}[\/latex]<\/li>\n \t<li>[latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rcrrrrrr}\n&amp;24x^2&amp;+&amp;11x&amp;-&amp;80&amp;=&amp;3x \\\\\n&amp;&amp;-&amp;3x&amp;&amp;&amp;&amp;-3x \\\\\n\\hline\n&amp;24x^2&amp;+&amp;8x&amp;-&amp;80&amp;=&amp;0 \\\\\n&amp;8(3x^2&amp;+&amp;x&amp;-&amp;10)&amp;=&amp;0 \\\\\n8(3x&amp;-&amp;5)&amp;(x&amp;+&amp;2)&amp;=&amp;0 \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;x&amp;=&amp;\\dfrac{5}{3} \\\\ \\\\\n&amp;&amp;&amp;&amp;&amp;x&amp;=&amp;-2\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"<ol>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rr} \\begin{array}[t]{rrrrr} k&-&7&=&0 \\\\ &+&7&&+7 \\\\ \\hline &&k&=&7 \\end{array} &\\hspace{0.25in} \\begin{array}[t]{rrrrr} k&+&2&=&0 \\\\ &-&2&&-2 \\\\ \\hline &&k&=&-2 \\end{array} \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rr} \\begin{array}[t]{rrrrr} a&+&4&=&0 \\\\ &-&4&&-4 \\\\ \\hline &&a&=&-4 \\end{array} &\\hspace{0.25in} \\begin{array}[t]{rrrrr} a&-&3&=&0 \\\\ &+&3&&+3 \\\\ \\hline &&a&=&3 \\end{array} \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rr} \\begin{array}[t]{rrrrr} x&-&1&=&0 \\\\ &+&1&&+1 \\\\ \\hline &&x&=&1 \\end{array} &\\hspace{0.25in} \\begin{array}[t]{rrrrr} x&+&4&=&0 \\\\ &-&4&&-4 \\\\ \\hline &&x&=&-4 \\end{array} \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rr} \\begin{array}[t]{rrrrr} 2x&+&5&=&0 \\\\ &-&5&&-5 \\\\ \\hline &&\\dfrac{2x}{2}&=&\\dfrac{-5}{2} \\\\ \\\\ &&x&=&-\\dfrac{5}{2} \\end{array} &\\hspace{0.25in} \\begin{array}[t]{rrrrr} x&-&7&=&0 \\\\ &+&7&&+7 \\\\ \\hline &&x&=&7 \\end{array} \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrr} 6(x^2-25)&=&0 \\\\ 6(x-5)(x+5)&=&0 \\\\ \\\\ x&=&5 \\\\ x&=&-5 \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrr} (p+8)(p-4)&=&0 \\\\ \\\\ p&=&-8 \\\\ p&=&4 \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrr} 2(n^2+5n-14)&=&0 \\\\ 2(n+7)(n-2)&=&0 \\\\ \\\\ n&=&-7 \\\\ n&=&2 \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrr} (m-6)(m+5)&=&0 \\\\ \\\\ m&=&6 \\\\ m&=&-5 \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrr} (x+3)(7x+5)&=&0 \\\\ \\\\ x&=&-3 \\\\ x&=&-\\dfrac{5}{7} \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrr} (2b+1)(b-2)&=&0 \\\\ \\\\ b&=&-\\dfrac{1}{2} \\\\ \\\\ b&=&2 \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrr} x^2&-&4x&-&8&=&-8 \\\\ &&&+&8&&+8 \\\\ \\hline &&x^2&-&4x&=&0 \\\\ &&x(x&-&4)&=&0 \\\\ \\\\ &&&&x&=&0 \\\\ &&&&x&=&4 \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrr} v^2&-&8v&-&3&=&-3 \\\\ &&&+&3&&+3 \\\\ \\hline &&v^2&-&8v&=&0 \\\\ &&v(v&-&8)&=&0 \\\\ \\\\ &&&&v&=&0 \\\\ &&&&v&=&8 \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrrr} &x^2&-&5x&-&1&=&-5 \\\\ &&&&+&5&&+5 \\\\ \\hline &x^2&-&5x&+&4&=&0 \\\\ (x&-&4)&(x&-&1)&=&0 \\\\ \\\\ &&&&&x&=&4 \\\\ &&&&&x&=&1 \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrrr} &a^2&-&6a&+&6&=&-2 \\\\ &&&&+&2&=&+2 \\\\ \\hline &a^2&-&6a&+&8&=&0 \\\\ (a&-&4)&(a&-&2)&=&0 \\\\ \\\\ &&&&&a&=&4 \\\\ &&&&&a&=&2 \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrrr} &7x^2&+&17x&-&20&=&-8 \\\\ &&&&+&8&&+8 \\\\ \\hline &7x^2&+&17x&-&12&=&0 \\\\ (7x&-&4)&(x&+&3)&=&0 \\\\ \\\\ &&&&&x&=&\\dfrac{4}{7} \\\\ \\\\ &&&&&x&=&-3 \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrrr} &4n^2&-&13n&+&8&=&5 \\\\ &&&&-&5&&-5 \\\\ \\hline &4n^2&-&13n&+&3&=&0 \\\\ (4n&-&1)&(n&-&3)&=&0 \\\\ \\\\ &&&&&n&=&\\dfrac{1}{4} \\\\ \\\\ &&&&&n&=&3 \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrrr} &x^2&-&6x&&&=&16 \\\\ &&&&-&16&&-16 \\\\ \\hline &x^2&-&6x&-&16&=&0 \\\\ (x&-&8)&(x&+&2)&=&0 \\\\ \\\\ &&&&&x&=&8 \\\\ &&&&&x&=&-2 \\\\ \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrr} 7n^2&-&28n&=&0 \\\\ 7n(n&-&4)&=&0 \\\\ \\\\ &&n&=&0 \\\\ &&n&=&4 \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rcrrrrrrrr} &4k^2&+&22k&+&23&=&6k&+&7 \\\\ &&-&6k&-&7&&-6k&-&7 \\\\ \\hline &4k^2&+&16k&+&16&=&0&& \\\\ &4(k^2&+&4k&+&4)&=&0&& \\\\ 4(k&+&2)&(k&+&2)&=&0&& \\\\ \\\\ &&&&&k&=&-2&& \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrrrrr} &a^2&+&7a&-&9&=&-3&+&6a \\\\ &&-&6a&+&3&&+3&-&6a \\\\ \\hline &a^2&+&a&-&6&=&0&& \\\\ (a&+&3)&(a&-&2)&=&0&& \\\\ \\\\ &&&&&a&=&-3&& \\\\ &&&&&a&=&2&& \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrrrrrrr} &9x^2&-&46&+&7x&=&7x&+&8x^2&+&3 \\\\ &-8x^2&-&3&-&7x&&-7x&-&8x^2&-&3 \\\\ \\hline &&&x^2&-&49&=&0&&&& \\\\ (x&-&7)&(x&+&7)&=&0&&&& \\\\ \\\\ &&&&&x&=&7&&&& \\\\ &&&&&x&=&-7&&&& \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrrr} &x^2&+&10x&+&30&=&6 \\\\ &&&&-&6&=&-6 \\\\ \\hline &x^2&+&10x&+&24&=&0 \\\\ (x&+&6)&(x&+&4)&=&0 \\\\ \\\\ &&&&&x&=&-6 \\\\ &&&&&x&=&-4 \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rrrrrrrrrr} &40p^2&+&183p&-&168&=&p&+&5p^2 \\\\ &-5p^2&-&p&&&&-p&-&5p^2 \\\\ \\hline &35p^2&+&182p&-&168&=&0&& \\\\ &7(5p^2&+&26p&-&24)&=&0&& \\\\ 7(p&+&6)&(5p&-&4)&=&0&& \\\\ \\\\ &&&&&p&=&-6&& \\\\ \\\\ &&&&&p&=&\\dfrac{4}{5}&& \\end{array}[\/latex]<\/li>\n<li>[latex]\\phantom{a}[\/latex]<br \/>\n[latex]\\begin{array}[t]{rcrrrrrr} &24x^2&+&11x&-&80&=&3x \\\\ &&-&3x&&&&-3x \\\\ \\hline &24x^2&+&8x&-&80&=&0 \\\\ &8(3x^2&+&x&-&10)&=&0 \\\\ 8(3x&-&5)&(x&+&2)&=&0 \\\\ \\\\ &&&&&x&=&\\dfrac{5}{3} \\\\ \\\\ &&&&&x&=&-2 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