# How do you solve -19 = 30 - 7x^2?

Feb 10, 2017

See the entire solution process below:

#### Explanation:

First, subtract $\textcolor{red}{30}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$- \textcolor{red}{30} - 19 = - \textcolor{red}{30} + 30 - 7 {x}^{2}$

$- 49 = 0 - 7 {x}^{2}$

$- 49 = - 7 {x}^{2}$

Next, divide each side of the equation by $\textcolor{red}{- 7}$ to solve for ${x}^{2}$ while keeping the equation balanced:

$\frac{- 49}{\textcolor{red}{- 7}} = \frac{- 7 {x}^{2}}{\textcolor{red}{- 7}}$

$7 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 7}}} {x}^{2}}{\cancel{\textcolor{red}{- 7}}}$

$7 = {x}^{2}$

${x}^{2} = 7$

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 the number yields both a positive and a negative result:

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

$x = \pm \sqrt{7} = 2.646$ rounded to the nearest thousandth.