# How do you solve the equation 4x^2+1=a?

Feb 19, 2017

See the entire solution process below:

#### Explanation:

First, subtract $\textcolor{red}{1}$ from each side of the equation to isolate the ${x}^{2}$ term while keeping the equation balanced:

$4 {x}^{2} + 1 - \textcolor{red}{1} = a - \textcolor{red}{1}$

$4 {x}^{2} + 0 = a - 1$

$4 {x}^{2} = a - 1$

Next, divide each side of the equation by $\textcolor{red}{4}$ to isolate ${x}^{2}$ while keeping the equation balanced:

$\frac{4 {x}^{2}}{\textcolor{red}{4}} = \frac{a - 1}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} {x}^{2}}{\cancel{\textcolor{red}{4}}} = \frac{a - 1}{4}$

${x}^{2} = \frac{a - 1}{4}$

Now, take the square root of each side of the equation to solve for $x$. However, remember when taking the square root of a number there will be a negative and positive result:

$\sqrt{{x}^{2}} = \pm \sqrt{\frac{a - 1}{4}}$

$x = \pm \frac{\sqrt{a - 1}}{\sqrt{4}}$

$x = \pm \frac{\sqrt{a - 1}}{2}$ where $a - 1 \ge 0$ or $a \ge 1$

Because we cannot take the square root of a negative number.