# How do you solve sqrt(x + 3) = 2x + 1?

Aug 10, 2015

$x = \frac{- 3 \pm \sqrt{41}}{8}$

#### Explanation:

Given $\sqrt{x + 3} = 2 x + 1$

Square both sides:
$\textcolor{w h i t e}{\text{XXXX}}$$x + 3 = 4 {x}^{2} + 4 x + 1$

Subtract $\left(x + 3\right)$ from both sides (and reverse sides)
$\textcolor{w h i t e}{\text{XXXX}}$$4 {x}^{2} + 3 x - 2 = 0$

Using the quadratic formula (see below)
$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{- 3 \pm \sqrt{41}}{8}$

$\textcolor{w h i t e}{\text{XXXX}}$for any quadratic in the general form:
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$a {x}^{2} + b x + c = 0$
$\textcolor{w h i t e}{\text{XXXX}}$the solutions are given by the formula:
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$