To solve the equation [tex]\( (v + 8)^2 = 0 \)[/tex], let's break it down step by step:
1. Understand the equation: We have [tex]\( (v + 8)^2 = 0 \)[/tex]. This means that we are squaring the expression [tex]\( v + 8 \)[/tex] and setting it equal to zero.
2. Isolate the squared term: Since the square of any real number is zero only if the number itself is zero, we set the expression inside the square equal to zero:
[tex]\[
v + 8 = 0
\][/tex]
3. Solve for [tex]\( v \)[/tex]: To find the value of [tex]\( v \)[/tex] that makes this equation true, we simply solve for [tex]\( v \)[/tex]:
[tex]\[
v + 8 = 0 \\
v = -8
\][/tex]
Therefore, the solution to the equation [tex]\( (v + 8)^2 = 0 \)[/tex] is [tex]\( v = -8 \)[/tex].
4. Verify the solution: Let's substitute [tex]\( v = -8 \)[/tex] back into the original equation to verify:
[tex]\[
((-8) + 8)^2 = 0 \\
0^2 = 0
\][/tex]
This confirms that [tex]\( v = -8 \)[/tex] satisfies the equation.
So, the only solution to the equation is:
[tex]\[
\boxed{-8}
\][/tex]
Since you are asked to select all solutions and the options given are:
- 16
- -8
- 4
- 8
The only correct solution from the given options is -8.
