Let's solve the quadratic equation [tex]\(x^2 + 12x + 36 = 0\)[/tex].
To find the solutions to the quadratic equation, we can use the quadratic formula, which is given by:
[tex]\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}
\][/tex]
For the given equation [tex]\(x^2 + 12x + 36 = 0\)[/tex], we can identify the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] as follows:
- [tex]\(a = 1\)[/tex]
- [tex]\(b = 12\)[/tex]
- [tex]\(c = 36\)[/tex]
Now, let's compute the discriminant [tex]\(\Delta\)[/tex] of the quadratic equation:
[tex]\[
\Delta = b^2 - 4ac
\][/tex]
Substituting the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]:
[tex]\[
\Delta = 12^2 - 4 \cdot 1 \cdot 36 = 144 - 144 = 0
\][/tex]
Since the discriminant [tex]\(\Delta\)[/tex] is 0, there is exactly one real solution to the equation, which is given by:
[tex]\[
x = \frac{{-b}}{2a}
\][/tex]
Substituting the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[
x = \frac{{-12}}{2 \cdot 1} = \frac{{-12}}{2} = -6
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that solves the quadratic equation [tex]\(x^2 + 12x + 36 = 0\)[/tex] is:
[tex]\[
x = -6
\][/tex]
So, the correct answer to the given question is:
[tex]\[
x = -6
\][/tex]
