Sure! Let's solve the given quadratic equation step by step:
The quadratic equation to solve is:
[tex]\[
(x + 4)^2 = 25
\][/tex]
1. Take the square root of both sides:
To isolate [tex]\( (x + 4) \)[/tex], we need to take the square root of both sides of the equation. This gives us two potential solutions because the square root of a number can be positive or negative:
[tex]\[
\sqrt{(x + 4)^2} = \pm\sqrt{25}
\][/tex]
Simplifying, we get:
[tex]\[
x + 4 = \pm 5
\][/tex]
2. Solve the two resulting equations:
We now solve for [tex]\( x \)[/tex] from each of these two cases:
- Case 1: [tex]\( x + 4 = 5 \)[/tex]
[tex]\[
x = 5 - 4
\][/tex]
[tex]\[
x = 1
\][/tex]
- Case 2: [tex]\( x + 4 = -5 \)[/tex]
[tex]\[
x = -5 - 4
\][/tex]
[tex]\[
x = -9
\][/tex]
3. Write down the solutions:
The solutions to the equation [tex]\((x + 4)^2 = 25\)[/tex] are:
[tex]\[
x = 1 \quad \text{and} \quad x = -9
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{x = -9 \text{ and } x = 1}
\][/tex]
Thus, the correct choice from the given options is:
C. [tex]\( x = -9 \text{ and } x = 1 \)[/tex]
