How do you solve 2x^2-2=6?

Feb 15, 2017

See the entire solution process below:

Explanation:

First, add $\textcolor{red}{2}$ to each side of the equation to isolate the ${x}^{2}$ term while keeping the equation balanced:

$2 {x}^{2} - 2 + \textcolor{red}{2} = 6 + \textcolor{red}{2}$

$2 {x}^{2} - 0 = 8$

$2 {x}^{2} = 8$

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

$\frac{2 {x}^{2}}{\textcolor{red}{2}} = \frac{8}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} {x}^{2}}{\cancel{\textcolor{red}{2}}} = 4$

${x}^{2} = 4$

Now, take the square root of each side of the equation to solve for $x$ while keeping the equation balanced. Remember, when taking the square root of the number there are two solutions, one negative and one positive:

$\sqrt{{x}^{2}} = \pm \sqrt{4}$

$x = \pm \sqrt{4} = \pm 2$