To solve the quadratic equation [tex]\((x + 4)^2 = 25\)[/tex], let's follow these steps:
1. Recognize that [tex]\((x + 4)^2 = 25\)[/tex] is a perfect square equation. We can start by taking the square root of both sides of the equation.
2. Taking the square root of both sides gives us:
[tex]\[ x + 4 = \pm \sqrt{25} \][/tex]
3. Simplifying further, we know that [tex]\(\sqrt{25} = 5\)[/tex]. Therefore, we have:
[tex]\[ x + 4 = 5 \quad \text{or} \quad x + 4 = -5 \][/tex]
4. Solve each equation separately:
- For [tex]\( x + 4 = 5 \)[/tex]:
[tex]\[ x = 5 - 4 \][/tex]
[tex]\[ x = 1 \][/tex]
- For [tex]\( x + 4 = -5 \)[/tex]:
[tex]\[ x = -5 - 4 \][/tex]
[tex]\[ x = -9 \][/tex]
Thus, the solutions to the equation [tex]\((x + 4)^2 = 25\)[/tex] are [tex]\( x = -9 \)[/tex] and [tex]\( x = 1 \)[/tex].
Therefore, the correct answer is:
C. [tex]\(x = -9\)[/tex] and [tex]\(x = 1\)[/tex]
