To complete the square for the quadratic equation [tex]\(x^2 - 6x - 34 = 0\)[/tex], follow these steps:
1. Start with the quadratic equation in standard form:
[tex]\[
x^2 - 6x - 34 = 0
\][/tex]
2. Focus on the [tex]\(x^2 - 6x\)[/tex] part of the equation. Ignore the constant term (in this case, [tex]\(-34\)[/tex]) for now.
3. To complete the square, take the coefficient of [tex]\(x\)[/tex], which is [tex]\(-6\)[/tex], divide it by 2, and then square the result:
[tex]\[
\left(\frac{-6}{2}\right)^2 = (-3)^2 = 9
\][/tex]
4. This means [tex]\(9\)[/tex] needs to be added to [tex]\(x^2 - 6x\)[/tex] to transform it into a perfect square trinomial.
Therefore, the number that would have to be added to complete the square is:
[tex]\[
\boxed{9}
\][/tex]
