Answer:
[tex]x = - 4 \: or \: x = - 14[/tex]
Step-by-step explanation:
We have been given the equation
[tex](x + 9) {}^{2} = 25[/tex]
and we are asked to apply the square root property of equality to our given a equation and isolate the variable
First, take the square root of both sides of our equation
[tex] \sqrt{(x + 9) {}^{2} } = \sqrt{25} [/tex]
[tex]x + 9 = \: 15[/tex]
[tex]x + 9 = 5 \: or \: x + 9 = - 5[/tex]
[tex]x + 9 - 9 = 5 - 9 \: or \: x + 9 - 9 = - 5 - 9[/tex]
[tex]x = - 4 \: or \: x = - 14[/tex]
THEREFORE, THERE ARE TWO SOLUTIONS FOR OUR GIVEN EQUATION
[tex]x + 9 = 5 \: then \: x = - 4. \\ x + 9 = - 5 \: then \: x = - 14[/tex]
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