Solve x^4-8x^2-5=0

$$x ^ { 4 } - 8 x ^ { 2 } - 5 = 0$$

Solve for x (complex solution)

$$x=i\sqrt{\sqrt{21}-4}\approx 0.763266464i$$

$$x=-i\sqrt{\sqrt{21}-4}\approx -0-0.763266464i$$

$$x=-\sqrt{\sqrt{21}+4}\approx -2.929603334$$

$$x=\sqrt{\sqrt{21}+4}\approx 2.929603334$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-8t-5=0$$

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, -8 for b, and -5 for c in the quadratic formula.

$$t=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 1\left(-5\right)}}{2}$$

Do the calculations.

$$t=\frac{8±2\sqrt{21}}{2}$$

Solve the equation t=\frac{8±2\sqrt{21}}{2} when ± is plus and when ± is minus.

$$t=\sqrt{21}+4 t=4-\sqrt{21}$$

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

$$x=-\sqrt{\sqrt{21}+4} x=\sqrt{\sqrt{21}+4} x=-i\sqrt{-\left(4-\sqrt{21}\right)} x=i\sqrt{-\left(4-\sqrt{21}\right)}$$

Solve for x

$$x=-\sqrt{\sqrt{21}+4}\approx -2.929603334$$

$$x=\sqrt{\sqrt{21}+4}\approx 2.929603334$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-8t-5=0$$

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, -8 for b, and -5 for c in the quadratic formula.

$$t=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 1\left(-5\right)}}{2}$$

Do the calculations.

$$t=\frac{8±2\sqrt{21}}{2}$$

Solve the equation t=\frac{8±2\sqrt{21}}{2} when ± is plus and when ± is minus.

$$t=\sqrt{21}+4 t=4-\sqrt{21}$$

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

$$x=\sqrt{\sqrt{21}+4} x=-\sqrt{\sqrt{21}+4}$$