Chapter 12.5, Problem 17WE

To determine

Solve the quadratic equation.

Answer to Problem 17WE

  $y=-3\pm 2\sqrt{5}$

Explanation of Solution

Given:

The equation is :

  $\frac{{\left(y+3\right)}^2}{4}=5$

Calculation:

The given equation $\frac{{\left(y+3\right)}^2}{4}=5$ .

So,

  $\begin{array}{l}\Rightarrow \frac{{\left(y+3\right)}^2}{4}=5\\ \Rightarrow {\left(y+3\right)}^2=\mathrm{20...................}[\text{multiply 4 each side]}\\ \Rightarrow y+3=\pm \sqrt{20}\mathrm{...................}[\text{take square root each side]}\\ \Rightarrow y=-3\pm 2\sqrt{5}\mathrm{...................}[subtract\text{ 3 from each side]}\end{array}$