# How do you solve by completing the square: x^2 +2x - 24 =0?

Apr 3, 2015

Ad $24$ to both sides to clear the constant from the left side of the equation
${x}^{2} + 2 x = 24$

Remember that ${\left(x + 1\right)}^{2} = {x}^{2} + 2 x + 1$
so add $1$ to both sides in order to complete the square on the left side
${x}^{2} + 2 x + 1 = 24 + 1$

${\left(x + 1\right)}^{2} = 25$

Take the square root of both sides
$x + 1 = \pm 5$

Giving the solutions
$x = 4$ and $x = - 6$