Chapter 9.4, Problem 1CGP

To determine

Find the value of m.

Answer to Problem 1CGP

  $m=-4$ or $m=2$

Explanation of Solution

Given Information: $4{(m+1)}^2=36$

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

Calculation:

  $4{(m+1)}^2=36$

Now,

  ${(m+1)}^2=\frac{36}{4}$

Now,

  ${(m+1)}^2=9$

Now,

  ${(m+1)}^2-9=0$

As square root of 9 is 3.

  ${(m+1)}^2-3^2=0$

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

  $(m+1+3)(m+1-3)=0$

Now,

  $(m+4)(m-2)=0$

Now,

  $(m+4)=0$ or $(m-2)=0$

Hence,

  $m=-4$ or $m=2$