# How do you solve 144k^2+7=71?

Dec 22, 2016

$k = \frac{2}{3}$

#### Explanation:

$144 {k}^{2} + 7 = 71$

subtract 7:

$144 {k}^{2} = 64$

divide by 144:

${k}^{2} = \frac{64}{144} = \frac{4}{9}$

square root:

$k = \pm \frac{2}{3}$

Dec 22, 2016

$k = \pm \frac{2}{3}$

#### Explanation:

Isolate $144 {k}^{2}$ by subtracting 7 from both sides.

$144 {k}^{2} \cancel{+ 7} \cancel{- 7} = 71 - 7$

$\Rightarrow 144 {k}^{2} = 64$

divide both sides of the equation by 144

$\frac{\cancel{144} {k}^{2}}{\cancel{144}} = \frac{64}{144}$

$\Rightarrow {k}^{2} = \frac{64}{144}$

To solve for k, take the $\textcolor{b l u e}{\text{square root of both sides}}$

$\sqrt{{k}^{2}} = \pm \sqrt{\frac{64}{144}}$

$\Rightarrow k = \pm \frac{8}{12} = \pm \frac{2}{3}$

$\Rightarrow k = - \frac{2}{3} \text{ or " k=2/3" are the solutions}$