# How do you solve using the completing the square method x^2 + 4x = 6?

Apr 1, 2018

$x = - 2 \pm \sqrt{10}$

#### Explanation:

When wanting to complete the square for a quadratic in the form

$a {x}^{2} + b x = c$, we add ${\left(\frac{b}{2}\right)}^{2}$ to each side and factor the left side. To solve, we can take the root of both sides, accounting for positive and negative answers on the right side.

In this case, $b = 4 , {\left(\frac{b}{2}\right)}^{2} = {\left(\frac{4}{2}\right)}^{2} = {2}^{2} = 4$, so we add $4$ to each side.

${x}^{4} + 4 x + 4 = 6 + 4$

Factoring ${x}^{4} + 4 x + 4$ yields ${\left(x + 2\right)}^{2}$

${\left(x + 2\right)}^{2} = 10$

So, take the root of both sides, account for positive and negative:

$\sqrt{{\left(x + 2\right)}^{2}} = \pm \sqrt{10}$

The root of a squared term is just that term:

$x + 2 = \pm \sqrt{10}$

$x = - 2 \pm \sqrt{10}$