[tex]$
\sqrt{(x+9)^2} = \pm \sqrt{25}
$[/tex]

If [tex]$x+9=5$[/tex], then [tex]$x=$[/tex] [tex]$\square$[/tex]

If [tex]$x+9=-5$[/tex], then [tex]$x=$[/tex] [tex]$\square$[/tex]



Answer :

Let's solve the equation step by step.

Given equation:
[tex]\[ \sqrt{(x+9)^2} = \pm \sqrt{25} \][/tex]

To solve this, we need to consider both possible scenarios separately:

### Case 1: [tex]\( \sqrt{(x+9)^2} = \sqrt{25} \)[/tex]
In this case, we have:
[tex]\[ (x+9)^2 = 25 \][/tex]
Taking the square root on both sides (considering the principal square root):
[tex]\[ x + 9 = 5 \][/tex]
Now, solving for [tex]\( x \)[/tex]:
[tex]\[ x = 5 - 9 \][/tex]
[tex]\[ x = -4 \][/tex]

### Case 2: [tex]\( \sqrt{(x+9)^2} = -\sqrt{25} \)[/tex]
In this case, we have:
[tex]\[ (x+9)^2 = 25 \][/tex]
Taking the square root on both sides (considering the negative square root):
[tex]\[ x + 9 = -5 \][/tex]
Now, solving for [tex]\( x \)[/tex]:
[tex]\[ x = -5 - 9 \][/tex]
[tex]\[ x = -14 \][/tex]

Hence, the solutions to the equation are:

If [tex]\( x+9=5 \)[/tex], then [tex]\( x= -4 \)[/tex].

If [tex]\( x+9=-5 \)[/tex], then [tex]\( x= -14 \)[/tex].