Question 204560
Solve for x:
{{{x^4-2x^2 = 8}}} Subtract 8 from both sides of the equation.
{{{x^4-2x^2-8 = 0}}} Now you can make this look like a quadratic equation by temporarily substituting {{{x^2 = z}}}
{{{z^2-2z-8 = 0}}} Factor this.
{{{(z+2)(z-4) = 0}}} Apply the zero product rule.
{{{z+2 = 0}}} or {{{z-4 = 0}}} which means that...
{{{z = -2}}} or {{{z = 4}}} Re-substitute {{{z = x^2}}} to get:
{{{x^2 = -2}}} or {{{x^2 = 4}}} so this means that...
{{{x = sqrt(-2)}}} or {{{x = -sqrt(-2)}}} or {{{x = 2}}} or {{{x = -2}}}