# How do you solve x^2 + 8x = 14 by completing the square?

Apr 29, 2015

${x}^{2} + 8 x = 14$

To write the Left Hand Side as a Perfect Square, we add 16 to both sides

${x}^{2} + 8 x + 16 = 14 + 16$

${x}^{2} + 2 \cdot 4 \cdot x + {4}^{2} = 30$

Using the Identity color(blue)((a+b)^2 = a^2 + 2ab + b^2, we get

${\left(x + 4\right)}^{2} = 30$

$x + 4 = \sqrt{30}$ or $x + 4 = - \sqrt{30}$

color(green)(x = sqrt 30 - 4 or  color(green)(x = -sqrt 30 + 4