Chapter 9.4, Problem 25PPS

To determine

Find the solution.

Answer to Problem 25PPS

$x=-2$ or $x=6$

Explanation of Solution

Given Information: ${\left(x-2\right)}^2=16$

Formula Used: $a^2-b^2=(a+b)(a-b)$

Calculation:

  ${\left(x-2\right)}^2=16$

So,

  ${\left(x-2\right)}^2-16=0$

Now, square root of 16 is 4.

  ${\left(x-2\right)}^2-{\left(4\right)}^2=0$

Now use formula, $a^2-b^2=(a+b)(a-b)$

  $\left(x-2+4\right)\left(x-2-4\right)=0$

Now,

  $\left(x+2\right)\left(x-6\right)=0$

Now,

$x+2=0$ or $x-6=0$

Hence,

$x=-2$ or $x=6$