# How do you complete the square to solve x^2 + 4x = 12?

May 31, 2015

${x}^{2} + 4 x = 12$

To write the Left Hand Side as a Perfect Square, we add 4 to both sides:

${x}^{2} + 4 x + 4 = 12 + 4$
${x}^{2} + 2 \cdot 2 \cdot x + {2}^{2} = 16$
Using the Identity color(blue)((a+b)^2 = a^2 + 2ab + b^2, we get
${\left(x + 2\right)}^{2} = 16$
$x + 2 = + \sqrt{16}$ or $x + 2 = - \sqrt{16}$
$x = + 4 - 2 \mathmr{and} - 4 - 2$
color(blue)(x = 2 or x=-6