To find an equivalent equation in the form [tex]\((x - h)^2 = k\)[/tex] for the given equation [tex]\(x^2 - 6x = 8\)[/tex], we will complete the square.
Here are the steps involved:
1. Start with the given equation:
[tex]\[
x^2 - 6x = 8
\][/tex]
2. Move the constant to the other side:
[tex]\[
x^2 - 6x - 8 = 0
\][/tex]
3. To complete the square: Focus on the terms involving [tex]\(x\)[/tex]. Take the coefficient of [tex]\(x\)[/tex], which is -6, and halve it, then square it:
[tex]\[
\left( \frac{-6}{2} \right)^2 = 9
\][/tex]
4. Add and subtract this square within the equation:
[tex]\[
x^2 - 6x + 9 = 8 + 9
\][/tex]
5. Simplify both sides:
[tex]\[
(x - 3)^2 = 17
\][/tex]
This results in the completed square form.
6. So, the equation equivalent to the given [tex]\(x^2 - 6x = 8\)[/tex] is:
[tex]\[
(x - 3)^2 = 17
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{(x-3)^2=17}
\][/tex]
Selecting from the options provided, the correct choice is:
[tex]\[
\boxed{\text{B}}
\][/tex]
