Question

Solve the quadratic equation using square root property.

$2q^2+5=30$.

Short answer

The solutions are$q=\pm \frac{5\sqrt{2}}{2}$.

Step-by-step solution

Given Information.  

The Given equation is$2q^2+5=30$.

Isolate the quadratic term and makes its coefficient one.   

$$\begin{gathered} 2q^2=30-52 \\ {q}^2=25 \\ {q}^2=\frac{25}{2} \end{gathered}$$

 Use the square root property.   

$$\begin{gathered} q=\pm \sqrt{\frac{25}{2}} \\ q=\pm \frac{5}{\sqrt{2}} \end{gathered}$$

Rationalize the denominator.

$$\begin{gathered} q=\pm \frac{5}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}} \\ q=\pm \frac{5\sqrt{2}}{2} \end{gathered}$$

Check the solutions.   

Substitute $q=\frac{5\sqrt{2}}{2}$.

$$\begin{gathered} 2q^2+5=30 \\ 2{\left(\frac{5\sqrt{2}}{2}\right)}^2+5\stackrel{?}{=}30 \\ 25+5\stackrel{?}{=}30 \\ 30=30True \end{gathered}$$

Substitute $q=-\frac{5\sqrt{2}}{2}$

$$\begin{gathered} 2q^2+5=30 \\ 2{\left(-\frac{5\sqrt{2}}{2}\right)}^2+5\stackrel{?}{=}30 \\ 25+5\stackrel{?}{=}30 \\ 30=30True \end{gathered}$$