# How do you solve the quadratic equation by completing the square: x^2 + 24 = - 10x?

Jul 17, 2015

I found:
${x}_{1} = - 4$
${x}_{2} = - 6$

#### Explanation:

Try this:
${x}^{2} + 10 x = - 24$
add and subtract $25$:
${x}^{2} + 10 x \textcolor{red}{+ 25 - 25} = - 24$
rearrange:
${x}^{2} + 10 x + 25 = 25 - 24$
${\left(x + 5\right)}^{2} = 1$
square root both sides:
${x}^{2} + 5 = \pm \sqrt{1} = \pm 1$
so you get two solutions:
${x}_{1} = - 5 + 1 = - 4$
${x}_{2} = - 5 - 1 = - 6$