To solve the quadratic equation [tex]\((x+4)^2 = 25\)[/tex], follow these steps:
1. Isolate the squared term:
[tex]\[
(x + 4)^2 = 25
\][/tex]
2. Take the square root of both sides to remove the square on the left side. When you take the square root of both sides, remember to consider both the positive and negative roots:
[tex]\[
x + 4 = \pm \sqrt{25}
\][/tex]
3. Calculate the square roots:
[tex]\[
\sqrt{25} = 5
\][/tex]
[tex]\[
\pm \sqrt{25} = \pm 5
\][/tex]
So, we have two equations:
[tex]\[
x + 4 = 5
\][/tex]
and
[tex]\[
x + 4 = -5
\][/tex]
4. Solve for [tex]\(x\)[/tex] in both cases:
- First case: [tex]\( x + 4 = 5 \)[/tex]
[tex]\[
x = 5 - 4
\][/tex]
[tex]\[
x = 1
\][/tex]
- Second case: [tex]\( x + 4 = -5 \)[/tex]
[tex]\[
x = -5 - 4
\][/tex]
[tex]\[
x = -9
\][/tex]
The solutions to the equation are [tex]\( x = 1 \)[/tex] and [tex]\( x = -9 \)[/tex].
Hence, the correct answer is:
[tex]\[ C. \ x = -9 \ \text{and} \ x = 1 \][/tex]
