Question

Solve the quadratic equation using square root property.

$\frac{3}{2}{b}^2-7=41$.

Short answer

The solutions are$b=\pm 4\sqrt{2}$

Step-by-step solution

Given Information.  

The Given equation is$\frac{3}{2}{b}^2-7=41$.

Isolate the quadratic term and makes its coefficient one.  

$$\begin{gathered} \frac{3}{2}{b}^2=41+7 \\ \frac{3}{2}{b}^2=48 \end{gathered}$$

Divide both sides by$\frac{3}{2}$.

$$\begin{gathered} b^2=48\times \frac{2}{3} \\ {b}^2=32 \end{gathered}$$

 Use the square root property.  

$$\begin{gathered} b=\sqrt{32} \\ b=\pm \sqrt{4·4·2} \\ b=\pm 4\sqrt{2} \end{gathered}$$

Check the solutions.  

Substitute $b=4\sqrt{2}$

role="math" localid="1648459422084" $$\begin{gathered} \frac{3}{2}(4\sqrt{2}{)}^2-7\stackrel{?}{=}41 \\ \frac{3}{2}(32)-7\stackrel{?}{=}41 \\ 48-7\stackrel{?}{=}41 \\ 41=41True \end{gathered}$$

Substitute $b=-4\sqrt{2}$

role="math" localid="1648459415015" $$\begin{gathered} \frac{3}{2}(-4\sqrt{2}{)}^2-7\stackrel{?}{=}41 \\ \frac{3}{2}(32)-7\stackrel{?}{=}41 \\ 48-7\stackrel{?}{=}41 \\ 41=41True \end{gathered}$$