Answer :
We want to solve the quadratic equation:
[tex]x^2-8x-7=0[/tex]by completing the square. For doing so, we will add a number to both sides for getting a square number at the left side. As the number at the side of the x is -8, when we divide by 2, we get:
[tex]\frac{8}{2}=4[/tex]We want to convert the number -7 to 16, so we will add 26 both sides:
[tex]\begin{gathered} x^2-8x-7+23=23 \\ x^2-8x+16=23 \\ (x-4)^2=23 \end{gathered}[/tex]And as we want to transform into the form:
[tex](x-p)^2=q[/tex]This means that p=4 and q=23.