Question

Solve the quadratic equation using square root property.

$v^2+18v+81=50$

Short answer

The solutions are$v=-9\pm 5\sqrt{2}$.

Step-by-step solution

Given Information.    

The Given equation is $v^2+18v+81=50$.

Factor the trinomial.     

$$\begin{gathered} v^2+2\left(9\right)v+(9{)}^2=50 \\ (v+9{)}^2=50 \end{gathered}$$

Use the square root property.

$v+9=\pm \sqrt{50}$

Factor the radical.

$$\begin{gathered} v+9=\pm \sqrt{2\times 5\times 5} \\ v+9=\pm 5\sqrt{2} \end{gathered}$$

Isolate the term.   

Subtract $9$from both sides.

$v=-9\pm 5\sqrt{2}$

Rewrite to show two solutions.

$$\begin{gathered} v=-9+5\sqrt{2}, \\ v=-9-5\sqrt{2} \end{gathered}$$