To convert the quadratic equation [tex]\(x^2 - 8x + 13 = 0\)[/tex] into the form [tex]\((x - p)^2 = q\)[/tex], where [tex]\(p\)[/tex] and [tex]\(q\)[/tex] are integers, we need to complete the square.
Let's go through the steps:
1. Move the constant term to the right-hand side:
[tex]\[
x^2 - 8x + 13 = 0
\][/tex]
The constant term in the equation is [tex]\(+13\)[/tex]. To isolate the terms involving [tex]\(x\)[/tex], we need to subtract 13 from both sides of the equation:
[tex]\[
x^2 - 8x + 13 - 13 = 0 - 13
\][/tex]
Simplifying both sides, we get:
[tex]\[
x^2 - 8x = -13
\][/tex]
Thus, the first correct step to write the given quadratic equation in the form [tex]\((x - p)^2 = q\)[/tex] is:
[tex]\[
x^2 - 8x + 13 - 13 = 0 - 13
\][/tex]
This corresponds with the answer choice [tex]\(x^2 - 8x + 13 - 13 = 0 - 13\)[/tex].
