# How do you solve a^2+3=51?

Jul 2, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{3}$ from each side of the equation to isolate the $a$ term while keeping the equation balanced:

${a}^{2} + 3 - \textcolor{red}{3} = 51 - \textcolor{red}{3}$

${a}^{2} + 0 = 48$

${a}^{2} = 48$

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

$\sqrt{{a}^{2}} = \pm \sqrt{48}$

$a = \pm \sqrt{48}$

We can rewrite the radical and simplify using this rule for radicals:

$\sqrt{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{a}} \cdot \sqrt{\textcolor{b l u e}{b}}$

$a = \pm \sqrt{16 \cdot 3}$

$a = \pm \sqrt{16} \cdot \sqrt{3}$

$a = \pm 4 \sqrt{12}$

If necessary, the numerical answer is:

$a = \pm 6.928$ rounded to the nearest thousandth