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} (3(x-7)^2)/(3)=(-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√(-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}`