# How do you solve  x^2 + 14x - 15 = 0 by completing the square?

Apr 4, 2016

The solutions are:
color(green)(x = 1 or  color(green)(x = -15

#### Explanation:

${x}^{2} + 14 x - 15 = 0$

${x}^{2} + 14 x = 15$

To write the Left Hand Side as a Perfect Square, we add $49$ to both sides:

${x}^{2} + 14 x + 49 = 15 + 49$

${x}^{2} + 2 \cdot x \cdot 7 + {7}^{2} = 64$

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

${\left(x + 7\right)}^{2} = 64$

$x + 7 = \sqrt{64}$ or $x + 7 = - \sqrt{64}$

color(green)(x = 8-7 = 1 or  color(green)(x = -8 - 7 = -15