Chapter 9.4, Problem 1AGP

To determine

Find the value of x.

Answer to Problem 1AGP

$x=-15$ or $x=3$

Explanation of Solution

Given Information: ${(x+6)}^2=81$

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

Calculation:

  ${(x+6)}^2=81$

As square root of 81 is 9.

  ${(x+6)}^2=9^2$

Now,

  ${(x+6)}^2-9^2=0$

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

  $(x+6+9)(x+6-9)=0$

Now,

  $(x+15)(x-3)=0$

Hence,

$x=-15$ or $x=3$