Seven less than 4 times the square of a number is 18. How do you find the number?

May 23, 2018

See a solution process below:

Explanation:

"the of square of a number" -> ${n}^{2}$

"4 times the of square of a number" -> $4 {n}^{2}$

"seven less than 4 times the of square of a number" -> $4 {n}^{2} - 7$

"seven less than 4 times the of square of a number is 18" -> $4 {n}^{2} - 7 = 18$

First, add $\textcolor{red}{7}$ to each side of the equation to isolate the $n$ term while keeping the equation balanced:

$4 {n}^{2} - 7 + \textcolor{red}{7} = 18 + \textcolor{red}{7}$

$4 {n}^{2} - 0 = 25$

$4 {n}^{2} = 25$

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

$\frac{4 {n}^{2}}{\textcolor{red}{4}} = \frac{25}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} {n}^{2}}{\cancel{\textcolor{red}{4}}} = \frac{25}{4}$

${n}^{2} = \frac{25}{4}$

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

$\sqrt{{n}^{2}} = \pm \sqrt{\frac{25}{4}}$

$n = \pm \frac{\sqrt{25}}{\sqrt{4}}$

$n = \pm \frac{5}{2}$

The number is $- \frac{5}{2}$ or $\frac{5}{2}$