# How do you solve x^2 - 4x = -3 by completing the square?

Oct 11, 2017

$x = 3$ OR $x = 1$

#### Explanation:

We want to add a number on both sides of the equation so that the left side becomes a perfect square:

To do that, we look at $b$ (the number next to $x$) and see that it is $- 4$

If you add ${\left(\frac{b}{2}\right)}^{2}$ to both sides, the equation on the left will be a perfect square or:

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

So:

${x}^{2} - 4 x \textcolor{red}{+ 4} = - 3 \textcolor{red}{+ 4}$

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

$\sqrt{{\left(x - 2\right)}^{2}} = \sqrt{1}$

$x - 2 = 1$ OR $x - 2 = - 1$

$x = 3$ OR $x = 1$