# How do you solve x^2 - 4x - 7 = 0 by completing the square?

Oct 5, 2016

#### Answer:

${\left(x - 2\right)}^{2} = 11$

#### Explanation:

The process of completing the square converts the quadratic equation into a perfect square trinomial.

First move the constant, $7$ to the other side of equation by addition.

${x}^{2} - 4 x = 7$

Next take the coefficient of the $x$ term and divide it by 2 and then square it.

${\left(- \frac{4}{2}\right)}^{2} = {\left(- 2\right)}^{2} = 4$

$4$ is amount needed to make the equation into a perfect square trinomial. Add $4$ to both sides of the equation to keep it balanced.

${x}^{2} - 4 x + 4 = 7 + 4$

Simplify

${x}^{2} - 4 x + 4 = 11$

Condense the equation

${\left(x - 2\right)}^{2} = 11$

Check out this tutorial on completing the square graphically.

Check out this tutorial on completing the square analytically.