Question

solve the equation by using the square root method$3(x - 7) {}^{2} + 10 = - 65$

Answer 1

First, subtract 10 on both sides of the equation

$\begin{gathered} 3(x-7)^2+10=-65 \\ 3(x-7)^2+10-10=-65-10 \\ 3(x-7)^2=-75 \end{gathered}$

Now divide by 3 both sides of the equation

$\begin{gathered} \frac{3(x-7)^2}{3}=\frac{-75}{3} \\ (x-7)^2=-25 \end{gathered}$

Now apply square root to both sides of the equation

$\begin{gathered} (x-7)^2=-25 \\ \sqrt[]{(x-7)^2}=\pm\sqrt{-25} \\ x-7=\pm\sqrt[]{25}\cdot\sqrt[]{-1} \\ x-7=\pm5i \end{gathered}$

Finally, add 7 on both sides of the equation

$\begin{gathered} x-7=\pm5i \\ x-7+7=\pm5i+7 \\ x=\pm5i+7 \end{gathered}$

Therefore, the solutions for x are

$\begin{gathered} x_1=5i+7 \\ x_2=-5i+7 \end{gathered}$