# Question #3b81a

Jan 17, 2015

Alright, let's re-write the first problem.

${x}^{2} + 4 x = 10$

Okay, we have a quadratic equation. The purpose of "completing the square" is to add a constant to both sides of the equation so that we can turn the left side into some form of ${\left(x + a\right)}^{2}$ , which is much easier to solve.

Let's go step by step.

First, take the half of the $x$ coefficient.

$\frac{4}{2} = 2$

Second, square it.

${2}^{2} = 4$

Third, add that result to both sides of the equation.

${x}^{2} + 4 x + 4 = 14$

Notice anything about the left side of the equation? It can be simplified into a form like ${\left(x + a\right)}^{2}$ In this case,

${\left(x + 2\right)}^{2} = 14$

which is much easier to solve than what we had originally.

$x + 2 = \pm \sqrt{14}$

$x = \sqrt{14} - 2$

$x = - \sqrt{14} - 2$