# How do you solve using the completing the square method x^2+8x=20?

Mar 9, 2016

The solutions are:
$x = 2$ ,
$x = - 10$

#### Explanation:

${x}^{2} + 8 x = 20$

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

${x}^{2} + 8 x + 16 = 20 + 16$

${x}^{2} + 2 \cdot 4 \cdot x + {4}^{2} = 36$

Using the Identity color(blue)((a+b)^2 = a^2 + 2ab + b^2, we get
${\left(x + 4\right)}^{2} = 36$

$x + 4 = \sqrt{36}$ or $x + 4 = - \sqrt{36}$

$x = 6 - 4$ or $x = - 6 - 4$

$x = 2$ or $x = - 10$

The solutions are:
$x = 2$ ,
$x = - 10$