Answer Key 7.8

$\begin{array}{rr} \\ \\ \begin{array}{rrrrr} k&-&7&=&0 \\ &+&7&&+7 \\ \midrule &&k&=&7 \end{array} &\hspace{0.25in} \begin{array}{rrrrr} k&+&2&=&0 \\ &-&2&&-2 \\ \midrule &&k&=&-2 \end{array} \end{array}$
$\begin{array}{rr} \\ \\ \begin{array}{rrrrr} a&+&4&=&0 \\ &-&4&&-4 \\ \midrule &&a&=&-4 \end{array} &\hspace{0.25in} \begin{array}{rrrrr} a&-&3&=&0 \\ &+&3&&+3 \\ \midrule &&a&=&3 \end{array} \end{array}$
$\begin{array}{rr} \\ \\ \begin{array}{rrrrr} x&-&1&=&0 \\ &+&1&&+1 \\ \midrule &&x&=&1 \end{array} &\hspace{0.25in} \begin{array}{rrrrr} x&+&4&=&0 \\ &-&4&&-4 \\ \midrule &&x&=&-4 \end{array} \end{array}$
$\begin{array}{rr} \\ \\ \begin{array}{rrrrr} \\ \\ \\ 2x&+&5&=&0 \\ &-&5&&-5 \\ \midrule &&\dfrac{2x}{2}&=&\dfrac{-5}{2} \\ \\ &&x&=&-\dfrac{5}{2} \end{array} &\hspace{0.25in} \begin{array}{rrrrr} x&-&7&=&0 \\ &+&7&&+7 \\ \midrule &&x&=&7 \end{array} \end{array}$
$\begin{array}{rrr} \\ \\ \\ \\ 6(x^2-25)&=&0 \\ 6(x-5)(x+5)&=&0 \\ \\ x&=&5 \\ x&=&-5 \end{array}$
$\begin{array}{rrr} \\ \\ \\ (p+8)(p-4)&=&0 \\ \\ p&=&-8 \\ p&=&4 \end{array}$
$\begin{array}{rrr} \\ \\ \\ \\ 2(n^2+5n-14)&=&0 \\ 2(n+7)(n-2)&=&0 \\ \\ n&=&-7 \\ n&=&2 \end{array}$
$\begin{array}{rrr} \\ \\ \\ (m-6)(m+5)&=&0 \\ \\ m&=&6 \\ m&=&-5 \end{array}$
$\begin{array}{rrr} \\ \\ \\ \\ (x+3)(7x+5)&=&0 \\ \\ x&=&-3 \\ x&=&-\dfrac{5}{7} \end{array}$
$\begin{array}{rrr} \\ \\ \\ \\ (2b+1)(b-2)&=&0 \\ \\ b&=&-\dfrac{1}{2} \\ \\ b&=&2 \end{array}$
$\begin{array}{rrrrrrr} \\ \\ \\ \\ \\ \\ x^2&-&4x&-&8&=&-8 \\ &&&+&8&&+8 \\ \midrule &&x^2&-&4x&=&0 \\ &&x(x&-&4)&=&0 \\ \\ &&&&x&=&0 \\ &&&&x&=&4 \end{array}$
$\begin{array}{rrrrrrr} \\ \\ \\ \\ \\ \\ v^2&-&8v&-&3&=&-3 \\ &&&+&3&&+3 \\ \midrule &&v^2&-&8v&=&0 \\ &&v(v&-&8)&=&0 \\ \\ &&&&v&=&0 \\ &&&&v&=&8 \end{array}$
$\begin{array}{rrrrrrrr} \\ \\ \\ \\ \\ \\ &x^2&-&5x&-&1&=&-5 \\ &&&&+&5&&+5 \\ \midrule &x^2&-&5x&+&4&=&0 \\ (x&-&4)&(x&-&1)&=&0 \\ \\ &&&&&x&=&4 \\ &&&&&x&=&1 \end{array}$
$\begin{array}{rrrrrrrr} \\ \\ \\ \\ \\ \\ &a^2&-&6a&+&6&=&-2 \\ &&&&+&2&=&+2 \\ \midrule &a^2&-&6a&+&8&=&0 \\ (a&-&4)&(a&-&2)&=&0 \\ \\ &&&&&a&=&4 \\ &&&&&a&=&2 \end{array}$
$\begin{array}{rrrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ &7x^2&+&17x&-&20&=&-8 \\ &&&&+&8&&+8 \\ \midrule &7x^2&+&17x&-&12&=&0 \\ (7x&-&4)&(x&+&3)&=&0 \\ \\ &&&&&x&=&\dfrac{4}{7} \\ \\ &&&&&x&=&-3 \end{array}$
$\begin{array}{rrrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ &4n^2&-&13n&+&8&=&5 \\ &&&&-&5&&-5 \\ \midrule &4n^2&-&13n&+&3&=&0 \\ (4n&-&1)&(n&-&3)&=&0 \\ \\ &&&&&n&=&\dfrac{1}{4} \\ \\ &&&&&n&=&3 \end{array}$
$\begin{array}{rrrrrrrr} \\ \\ \\ \\ \\ \\ &x^2&-&6x&&&=&16 \\ &&&&-&16&&-16 \\ \midrule &x^2&-&6x&-&16&=&0 \\ (x&-&8)&(x&+&2)&=&0 \\ \\ &&&&&x&=&8 \\ &&&&&x&=&-2 \\ \end{array}$
$\begin{array}{rrrrr} \\ \\ \\ \\ 7n^2&-&28n&=&0 \\ 7n(n&-&4)&=&0 \\ \\ &&n&=&0 \\ &&n&=&4 \end{array}$
$\begin{array}{rcrrrrrrrr} \\ \\ \\ \\ \\ \\ \\ &4k^2&+&22k&+&23&=&6k&+&7 \\ &&-&6k&-&7&&-6k&-&7 \\ \midrule &4k^2&+&16k&+&16&=&0&& \\ &4(k^2&+&4k&+&4)&=&0&& \\ 4(k&+&2)&(k&+&2)&=&0&& \\ \\ &&&&&k&=&-2&& \end{array}$
$\begin{array}{rrrrrrrrrr} \\ \\ \\ \\ \\ \\ &a^2&+&7a&-&9&=&-3&+&6a \\ &&-&6a&+&3&&+3&-&6a \\ \midrule &a^2&+&a&-&6&=&0&& \\ (a&+&3)&(a&-&2)&=&0&& \\ \\ &&&&&a&=&-3&& \\ &&&&&a&=&2&& \end{array}$
$\begin{array}{rrrrrrrrrrrr} \\ \\ \\ \\ \\ \\ &9x^2&-&46&+&7x&=&7x&+&8x^2&+&3 \\ &-8x^2&-&3&-&7x&&-7x&-&8x^2&-&3 \\ \midrule &&&x^2&-&49&=&0&&&& \\ (x&-&7)&(x&+&7)&=&0&&&& \\ \\ &&&&&x&=&7&&&& \\ &&&&&x&=&-7&&&& \end{array}$
$\begin{array}{rrrrrrrr} \\ \\ \\ \\ \\ \\ &x^2&+&10x&+&30&=&6 \\ &&&&-&6&=&-6 \\ \midrule &x^2&+&10x&+&24&=&0 \\ (x&+&6)&(x&+&4)&=&0 \\ \\ &&&&&x&=&-6 \\ &&&&&x&=&-4 \end{array}$
$\begin{array}{rrrrrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ &40p^2&+&183p&-&168&=&p&+&5p^2 \\ &-5p^2&-&p&&&&-p&-&5p^2 \\ \midrule &35p^2&+&182p&-&168&=&0&& \\ &7(5p^2&+&26p&-&24)&=&0&& \\ 7(p&+&6)&(5p&-&4)&=&0&& \\ \\ &&&&&p&=&-6&& \\ \\ &&&&&p&=&\dfrac{4}{5}&& \end{array}$
$\begin{array}{rcrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ &24x^2&+&11x&-&80&=&3x \\ &&-&3x&&&&-3x \\ \midrule &24x^2&+&8x&-&80&=&0 \\ &8(3x^2&+&x&-&10)&=&0 \\ 8(3x&-&5)&(x&+&2)&=&0 \\ \\ &&&&&x&=&\dfrac{5}{3} \\ \\ &&&&&x&=&-2 \end{array}$

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