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

May 26, 2016

$x = 1$ or $x = - 3$

#### Explanation:

In ${x}^{2} + 2 x$ a third term is missing to be able to write the square of a binomial.
Find it by dividing the coefficient of $x$ by 2, square it and add to both sides.

${x}^{2} + 2 x + \textcolor{red}{1} = 3 + \textcolor{red}{1}$

${\left(x + 1\right)}^{2} = 4$

$x + 1 = \pm \sqrt{4} = \pm 2$

$x = + 2 - 1$ or $x = - 2 - 1$

$x = 1$ or $x = - 3$