# How do you solve 3x^2-33=0?

Mar 6, 2018

See a solution process below:

#### Explanation:

First, add $\textcolor{red}{33}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$3 {x}^{2} - 33 + \textcolor{red}{33} = 0 + \textcolor{red}{33}$

$3 {x}^{2} - 0 = 33$

$3 {x}^{2} = 33$

Next, divide each side of the equation by $\textcolor{red}{3}$ to isolate the ${x}^{2}$ while keeping the equation balanced:

$\frac{3 {x}^{2}}{\textcolor{red}{3}} = \frac{33}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} {x}^{2}}{\cancel{\textcolor{red}{3}}} = 11$

${x}^{2} = 11$

Now, take the square root of each side of the equation to solve for $x$ while keeping the equation balanced. Remember, the square root of a number produces a positive and negative result:

$\sqrt{{x}^{2}} = \pm \sqrt{11}$

$x = \pm \sqrt{11}$

Or

$x = \pm 3.317$ rounded to the nearest thousandth.