To complete the square for the equation [tex]\(x^2 - 6x = 15\)[/tex], follow these steps:
1. Identify the coefficient of the [tex]\(x\)[/tex] term:
The given equation is [tex]\(x^2 - 6x = 15\)[/tex]. The coefficient of the [tex]\(x\)[/tex] term is [tex]\(-6\)[/tex].
2. Divide the coefficient of [tex]\(x\)[/tex] by 2:
[tex]\[
\frac{-6}{2} = -3
\][/tex]
3. Square the result:
[tex]\[
(-3)^2 = 9
\][/tex]
To complete the square, you add this squared result (which is 9) to both sides of the equation.
Thus, the number you would add to both sides in order to complete the square is:
[tex]\[
\boxed{9}
\][/tex]
The correct answer is (F) 9.
