Answer:
The solution to the given equation is
x = -1 OR -7
Explanation:
Given the equation:
[tex](x+4)^2-2=7[/tex]To solve this, first of all add 2 to both sides of the equation
[tex]\begin{gathered} (x+4)^2-2+2=7+2 \\ \\ (x+4)^2=9 \end{gathered}[/tex]Next, take square roots of both sides
[tex]\begin{gathered} \sqrt[]{(x+4)^2}=\pm\sqrt[]{9} \\ \\ x+4=\pm3 \end{gathered}[/tex]Subtract 4 from both sides
[tex]\begin{gathered} x+4-4=-4\pm3 \\ x=-4+3=-1 \\ OR \\ x=-4-3=-7 \end{gathered}[/tex]