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

Jul 15, 2015

Add the square of half the coefficient of $x$ to both sides; take the square root of both sides and perform standard arithmetic operations to get: $x = - 3 \mathmr{and} + 1$

#### Explanation:

Given ${x}^{2} + 2 x = 3$

Add the square of ($\frac{1}{2}$ of $2$)
$\textcolor{w h i t e}{\text{XXXX}}$${x}^{2} + 2 x + 1 = 3 + 1$

Rewrite the left side as a binomial square (and simplify the right side)
$\textcolor{w h i t e}{\text{XXXX}}$${\left(x + 1\right)}^{2} = 4$

Take the square root of both sides
$\textcolor{w h i t e}{\text{XXXX}}$$x + 1 = \pm 2$

Subtract $1$ from both sides
$\textcolor{w h i t e}{\text{XXXX}}$$x = - 3 \mathmr{and} + 1$