# How do you solve 4x^2-6=74?

Mar 3, 2018

$x = 2 \sqrt{5}$

#### Explanation:

We can begin by adding $6$ to both sides of this equation. Doing this, we get:

$4 {x}^{2} = 80$

We want to isolate $x$, so the next best step would be to divide both sides by $4$. We get:

${x}^{2} = 20$

Now, we can take the square root of both sides to get:

$x = \pm \sqrt{20}$ (We have a positive and negative answer because squaring a negative number will also result in a positive number)

We can factor out a perfect square from $\pm \sqrt{20}$.
$20$ is equal to $4 \cdot 5$, so $\sqrt{20}$ will be equal to $\sqrt{4} \cdot \sqrt{5}$. Now, we have:

$x = \pm \left(\textcolor{b l u e}{\sqrt{4}} \cdot \textcolor{red}{\sqrt{5}}\right)$

This simplifies to:

$x = \pm \textcolor{b l u e}{2} \textcolor{red}{\sqrt{5}}$