# How do you solve x^2+6x-16=0?

Mar 27, 2016

$x = 2$ or $x = - 8$

#### Explanation:

Find two factors of $16$ which differ by $6$. The pair $8 , 2$ works in that $8 \times 2 = 16$ and $8 - 2 = 6$.

Hence we find:

$0 = {x}^{2} + 6 x - 16 = \left(x + 8\right) \left(x - 2\right)$

So $x = 2$ or $x = - 8$

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Alternatively, complete the square then use the difference of squares identity:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

with $a = \left(x + 3\right)$ and $b = 5$ as follows:

$0 = {x}^{2} + 6 x - 16$

$= {\left(x + 3\right)}^{2} - 9 - 16$

$= {\left(x + 3\right)}^{2} - 25$

$= {\left(x + 3\right)}^{2} - {5}^{2}$

$= \left(\left(x + 3\right) - 5\right) \left(\left(x + 3\right) + 5\right)$

$= \left(x - 2\right) \left(x + 8\right)$

Hence zeros $x = 2$ and $x = - 8$