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

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

Solve for x

$$x=-\sqrt{4-\sqrt{11}}\approx -0.826665113$$

$$x=\sqrt{4-\sqrt{11}}\approx 0.826665113$$

$$x=\sqrt{\sqrt{11}+4}\approx 2.704926023$$

$$x=-\sqrt{\sqrt{11}+4}\approx -2.704926023$$

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.

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

Do the calculations.

$$t=\frac{8±2\sqrt{11}}{2}$$

Solve the equation t=\frac{8±2\sqrt{11}}{2} when ± is plus and when ± is minus.

$$t=\sqrt{11}+4 t=4-\sqrt{11}$$

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

$$x=\sqrt{\sqrt{11}+4} x=-\sqrt{\sqrt{11}+4} x=\sqrt{4-\sqrt{11}} x=-\sqrt{4-\sqrt{11}}$$