Question

Use the Square Root Method to solve the equation${\left(x-2\right)}^2=9$

Short answer

Values of$x$are$-1,5$.

Step-by-step solution

Step 1. Given information

An equation is${\left(x-2\right)}^2=9$.

Step 2. Solve the given equation.

Consider the equation $(x-2{)}^2=9$

The right hand side is already a perfect square, so we will take square root of both sides

role="math" localid="1646119886036" $\begin{array}{rcl}\sqrt{(x-2{)}^2}& =& \sqrt{9}\\ x-2& =& \pm 3\\ x-2& =& -3,x-2=3\\ x& =& -1,5\\ & & \end{array}$