# How do you solve x^2+2x-7=17 by completing the square?

May 15, 2015

Take $- 7$ to the right:
${x}^{2} + 2 x = 17 + 7$
${x}^{2} + 2 x = 24$
add and subtract $1$ to the left:
${x}^{2} + 2 x + 1 - 1 = 24$
$\left({x}^{2} + 2 x + 1\right) - 1 = 24$
${\left(x + 1\right)}^{2} - 1 = 24$
${\left(x + 1\right)}^{2} = 25$ take the square root of both sides and get rid of the ${\left(\right)}^{2}$:
$x + 1 = \pm \sqrt{25}$
$x = - 1 \pm 5$
So you get:
${x}_{1} = - 1 + 5 = 4$
${x}_{2} = - 1 - 5 = - 6$