# How do you solve 1/4b^2=16?

Apr 17, 2017

${b}^{2} = 64$ or $b = 8$

#### Explanation:

Expand both sides by 4:
$\frac{4 {b}^{2}}{4} = 4 \cdot 16$

Now you have
${b}^{2} = 64$

Take square root (both sides)
$\sqrt{{b}^{2}} = \sqrt{64}$

$b = 8$

Apr 17, 2017

$b = \pm 8$

#### Explanation:

$\textcolor{b l u e}{\text{Isolate " b^2" by multiplying both sides by 4}}$

${\cancel{4}}^{1} \times \frac{1}{\cancel{4}} ^ 1 {b}^{2} = 4 \times 16$

$\Rightarrow {b}^{2} = 64$

$\textcolor{b l u e}{\text{take the square root of both sides}}$

$\sqrt{{b}^{2}} = \textcolor{red}{\pm} \sqrt{64}$

$\Rightarrow b = \textcolor{red}{\pm} 8$

$\textcolor{b l u e}{\text{As a check}}$

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

$x = \textcolor{red}{+ 8} \to \frac{1}{4} \times {8}^{2} = \frac{1}{4} \times 64 = 16$

$x = \textcolor{red}{- 8} \to \frac{1}{4} \times {\left(- 8\right)}^{2} = \frac{1}{4} \times 64 = 16$

$\Rightarrow x = \pm 8 \text{ are the solutions}$