Solve x^4-x^2-20=0

$${ x }^{ 4 } - { x }^{ 2 } -20 = 0$$

Solve for x (complex solution)

$$x=\sqrt{5}\approx 2.236067977$$

$$x=-\sqrt{5}\approx -2.236067977$$

$$x=-2i$$

$$x=2i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-t-20=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, -1 for b, and -20 for c in the quadratic formula.

$$t=\frac{-\left(-1\right)±\sqrt{\left(-1\right)^{2}-4\times 1\left(-20\right)}}{2}$$

Do the calculations.

$$t=\frac{1±9}{2}$$

Solve the equation t=\frac{1±9}{2} when ± is plus and when ± is minus.

$$t=5 t=-4$$

Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for each t.

$$x=-\sqrt{5} x=\sqrt{5} x=-2i x=2i$$

Solve for x

$$x=-\sqrt{5}\approx -2.236067977$$

$$x=\sqrt{5}\approx 2.236067977$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-t-20=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, -1 for b, and -20 for c in the quadratic formula.

$$t=\frac{-\left(-1\right)±\sqrt{\left(-1\right)^{2}-4\times 1\left(-20\right)}}{2}$$

Do the calculations.

$$t=\frac{1±9}{2}$$

Solve the equation t=\frac{1±9}{2} when ± is plus and when ± is minus.

$$t=5 t=-4$$

Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for positive t.

$$x=\sqrt{5} x=-\sqrt{5}$$