Question

Solve each quadratic equation.f(x) = (x + 7)2 – 2

Answer 1

$f(x)=(x+2)^2-2$

Let's find the solutions:

$\begin{gathered} f(x)=0 \\ \mleft(x+7\mright)^2-2=0 \end{gathered}$

Solve for x:

Add 2 to both sides:

$\begin{gathered} (x+7)^2-2+2=0+2 \\ (x+7)^2=2 \end{gathered}$

Take the square root of both sides:

$\begin{gathered} \sqrt[]{(x+7)^2}=\pm\sqrt[]{2} \\ x+7=\pm\sqrt[]{2} \end{gathered}$

Subtract 7 from both sides:

$\begin{gathered} x+7-7=\pm\sqrt[]{2}-7 \\ x=\pm\sqrt[]{2}-7 \\ so\colon \\ x=\sqrt[]{2}-7\approx5.586 \\ x=-\sqrt[]{2}-7\approx-8.414 \end{gathered}$

You can verify the results using the graph: