Question 611369
{{{x^2=8x+2}}}
Whether you use the Quadratic formula or factoring, you want one side of the quadratic equation to be a zero. Subtracting 8x and 2 from each side we get:
{{{x^2-8x-2=0}}}
Now we can use the quadratic formula:
{{{x = (-(-8) +- sqrt((-8)^2 - 4(1)(-2)))/2(1)}}}
Simplifying:
{{{x = (-(-8) +- sqrt(64 - 4(1)(-2)))/2(1)}}}
{{{x = (-(-8) +- sqrt(64 + 8))/2(1)}}}
{{{x = (-(-8) +- sqrt(72))/2(1)}}}
{{{x = (8 +- sqrt(72))/2}}}
{{{x = (8 +- sqrt(36*2))/2}}}
{{{x = (8 +- sqrt(36)*sqrt(2))/2}}}
{{{x = (8 +- 6*sqrt(2))/2}}}
{{{x = (2(4 +- 3*sqrt(2)))/2}}}
{{{x = (cross(2)(4 +- 3*sqrt(2)))/cross(2)}}}
{{{x = 4 +- 3*sqrt(2)}}}
So the solutions to your equation are:
{{{x = 4 + 3*sqrt(2)}}} or {{{x = 4 - 3*sqrt(2)}}}