# How do you solve x^2 + 4x + 4 = 7 and simplify the answer in simplest radical form?

Jul 26, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{7}$ from each side of the equation to put the equation in standard form:

${x}^{2} + 4 x + 4 - \textcolor{red}{7} = 7 - \textcolor{red}{7}$

${x}^{2} + 4 x - 3 = 0$

We can now use the quadratic formula to find the solutions for $x$. The quadratic formula states:

For $\textcolor{red}{a} {x}^{2} + \textcolor{b l u e}{b} x + \textcolor{g r e e n}{c} = 0$, the values of $x$ which are the solutions to the equation are given by:

$x = \frac{- \textcolor{b l u e}{b} \pm \sqrt{{\textcolor{b l u e}{b}}^{2} - \left(4 \textcolor{red}{a} \textcolor{g r e e n}{c}\right)}}{2 \cdot \textcolor{red}{a}}$

Substituting:

$\textcolor{red}{1}$ for $\textcolor{red}{a}$

$\textcolor{b l u e}{4}$ for $\textcolor{b l u e}{b}$

$\textcolor{g r e e n}{- 3}$ for $\textcolor{g r e e n}{c}$ gives:

$x = \frac{- \textcolor{b l u e}{4} \pm \sqrt{{\textcolor{b l u e}{4}}^{2} - \left(4 \cdot \textcolor{red}{1} \cdot \textcolor{g r e e n}{- 3}\right)}}{2 \cdot \textcolor{red}{1}}$

$x = \frac{- \textcolor{b l u e}{4} \pm \sqrt{16 - \left(- 12\right)}}{2}$

$x = \frac{- \textcolor{b l u e}{4} \pm \sqrt{16 + 12}}{2}$

$x = \frac{- \textcolor{b l u e}{4} \pm \sqrt{28}}{2}$

$x = \frac{- \textcolor{b l u e}{4} \pm \sqrt{4 \cdot 7}}{2}$

$x = \frac{- \textcolor{b l u e}{4} \pm \sqrt{4} \sqrt{7}}{2}$

$x = \frac{- \textcolor{b l u e}{4} \pm 2 \sqrt{7}}{2}$

$x = - \frac{\textcolor{b l u e}{4}}{2} \pm \frac{2 \sqrt{7}}{2}$

$x = - 2 \pm \sqrt{7}$

Or

$x = - 2 + \sqrt{7}$ and $x = - 2 - \sqrt{7}$