To solve the equation [tex]\( x^2 - 18x + 58 = 0 \)[/tex] by completing the square, follow these steps:
1. Move the constant term to the other side of the equation:
[tex]\[
x^2 - 18x = -58
\][/tex]
2. Complete the square on the left side:
- Take the coefficient of [tex]\( x \)[/tex], which is [tex]\(-18\)[/tex], divide it by 2, and square the result.
[tex]\[
\left( \frac{-18}{2} \right)^2 = (-9)^2 = 81
\][/tex]
3. Add and subtract this square inside the equation:
[tex]\[
x^2 - 18x + 81 = -58 + 81
\][/tex]
4. Simplify both sides:
[tex]\[
x^2 - 18x + 81 = 23
\][/tex]
5. Rewrite the left side as the square of a binomial:
[tex]\[
(x - 9)^2 = 23
\][/tex]
6. Take the square root of both sides:
[tex]\[
x - 9 = \pm \sqrt{23}
\][/tex]
7. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = 9 \pm \sqrt{23}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{A. \ x = 9 \pm \sqrt{23}}
\][/tex]
