Solve x^4-4x^2-5=0

$$x ^ { 4 } - 4 x ^ { 2 } - 5 = 0$$

Solve for x (complex solution)

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

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

$$x=-i$$

$$x=i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-4t-5=0$$

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, -4 for b, and -5 for c in the quadratic formula.

$$t=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 1\left(-5\right)}}{2}$$

Do the calculations.

$$t=\frac{4±6}{2}$$

Solve the equation t=\frac{4±6}{2} when ± is plus and when ± is minus.

$$t=5 t=-1$$

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

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

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}.

$$t^{2}-4t-5=0$$

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, -4 for b, and -5 for c in the quadratic formula.

$$t=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 1\left(-5\right)}}{2}$$

Do the calculations.

$$t=\frac{4±6}{2}$$

Solve the equation t=\frac{4±6}{2} when ± is plus and when ± is minus.

$$t=5 t=-1$$

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

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