Chapter SH, Problem 9.16EP

To determine

To find: The solution of the equation ${\left(x-2\right)}^2=16$ .

Answer to Problem 9.16EP

The solutions of the equation ${\left(x-2\right)}^2=16$ are 4 and $-4$ .

Explanation of Solution

Given information:

The given equation is ${\left(x-2\right)}^2=16$ .

Calculation:

Solve the equation.

  $\begin{array}{c}{\left(x-2\right)}^2=16\\ x^2+4-4x=16\\ x^2-4x-12=0\end{array}$

Determine the factors of the above equation.

  $\begin{array}{c}{x}^2-6x+2x-12=0\\ x\left(x-6\right)+2\left(x-6\right)=0\\ \left(x-6\right)\left(x+2\right)=0\\ x=-2,6\end{array}$

So, the solutions of the equation ${\left(x-2\right)}^2=16$ are $-2$ and $6$ .

Therefore, the solutions of the equation ${\left(x-2\right)}^2=16$ are $-2$ and $6$ .