X^2–16x+64=8
Subtract 8 from both sides of the equation:
X^2–16x+64 -8=8-8
X^2–16x+56=0
Apply the quadratic formula:
[tex]\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where:
a=1 . b=-16 , c = 56
Replacing:
[tex]\frac{16\pm\sqrt[]{(-16)^2-4(1\times56)}}{2\times1}[/tex][tex]\frac{16\pm\sqrt[]{256-224}}{2}[/tex][tex]\frac{16\pm\sqrt[]{32}}{2}[/tex]positive:
[tex]\frac{16+\sqrt[]{32}}{2}=\frac{16+4\sqrt[]{2}}{2}\text{ = }8+2\sqrt[]{2}[/tex]Negative:
[tex]\frac{16-\sqrt[]{32}}{2}\text{ =}\frac{16-4\sqrt[]{2}}{2}=8-2\sqrt[]{2}[/tex]