# How do you solve 3+36p^2=103?

Feb 19, 2017

Collect like terms and move the numbers until the equation reads ${p}^{2} = \ldots$ Then, take the square root of both sides of the equation.

#### Explanation:

Here it is:

$36 {p}^{2} = 103 - 3$ (we subtract 3 from each side)

$36 {p}^{2} = 100$

Next, divide each side by 36

${p}^{2} = \frac{100}{36}$

(Resist the temptation to convert to decimals at this stage. It is actually easier with fractions!)

Square root:

$p = \sqrt{\frac{100}{36}} = \frac{\sqrt{100}}{\sqrt{36}} = \pm \frac{10}{6} = \pm \frac{5}{3}$

So, we have two answers (as expected!)

$\frac{5}{3}$ and $- \frac{5}{3}$

Feb 19, 2017

See the entire solution process below:

#### Explanation:

First, subtract $\textcolor{red}{3}$ from each side of the equation to isolate the ${p}^{2}$ term while keeping the equation balanced:

$- \textcolor{red}{3} + 3 + 36 {p}^{2} = - \textcolor{red}{3} + 103$

$0 + 36 {p}^{2} = 100$

$36 {p}^{2} = 100$

Next, divide each side of the equation by $\textcolor{red}{36}$ to isolate ${p}^{2}$ while keeping the equation balanced:

$\frac{36 {p}^{2}}{\textcolor{red}{36}} = \frac{100}{\textcolor{red}{36}}$

${p}^{2} = \frac{100}{36}$

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

$\sqrt{{p}^{2}} = \pm \sqrt{\frac{100}{36}}$

$p = \pm \frac{\sqrt{100}}{\sqrt{36}}$

$p = \pm \frac{10}{6}$

$p = \pm \frac{5}{3}$