How do you solve using the completing the square method x^2+2x-8=0?

Mar 31, 2016

The solutions are:
color(green)(x = 2 ,
 color(green)(x = -4

Explanation:

${x}^{2} + 2 x - 8 = 0$

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

To write the Left Hand Side as a Perfect Square, we add 1 to both sides:

${x}^{2} + 2 x + 1 = 8 + 1$

${x}^{2} + 2 \cdot x \cdot 1 + 1 = 9$

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

${\left(x + 1\right)}^{2} = 9$

$x + 1 = \sqrt{9}$ or $x + 1 = - \sqrt{9}$

color(green)(x = 3 -1 = 2 or  color(green)(x = -3 - 1 = -4