Question

Solve the quadratic equation using square root property.

$2d^2-4=77$

Short answer

The solutions are$d=\pm \frac{9\sqrt{2}}{2}$.

Step-by-step solution

Given Information.   

The Given equation is$2d^2-4=77$.

Isolate the binomial term.   

$$\begin{gathered} 2d^2=77+42 \\ {d}^2=81 \\ {d}^2=\frac{81}{2} \end{gathered}$$

Use the Square Root Property.    

$d=\pm \sqrt{\frac{81}{2}}$

Factor the radical.

$$\begin{gathered} d=\pm \sqrt{\frac{9\times 9}{2}} \\ d=\pm \frac{9}{\sqrt{2}} \end{gathered}$$

Rationalize the denominator. 

$$\begin{gathered} d=\pm \frac{9}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}} \\ d=\pm \frac{9\sqrt{2}}{2} \end{gathered}$$

Rewrite to show two solutions.

$$\begin{gathered} d=\frac{9\sqrt{2}}{2}, \\ d=-\frac{9\sqrt{2}}{2} \end{gathered}$$