# How do you solve x²+2x-24=0 algebraically?

Mar 21, 2016

Complete the square to find:

$x = 4$ or $x = - 6$

#### Explanation:

Complete the square ${x}^{2} + 2 x + 1$ then use the difference of squares identity:

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

with $a = \left(x + 1\right)$ and $b = 5$ as follows:

$0 = {x}^{2} + 2 x - 24$

$= {x}^{2} + 2 x + 1 - 1 - 24$

$= {\left(x + 1\right)}^{2} - {5}^{2}$

$= \left(\left(x + 1\right) - 5\right) \left(\left(x + 1\right) + 5\right)$

$= \left(x - 4\right) \left(x + 6\right)$

So $x = 4$ or $x = - 6$