Solve x^4-8x^2-9=0

$${ x }^{ 4 } -8 { x }^{ 2 } -9=0$$

Solve for x (complex solution)

$$x=3$$

$$x=-3$$

$$x=-i$$

$$x=i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-8t-9=0$$

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 -9 for c in the quadratic formula.

$$t=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 1\left(-9\right)}}{2}$$

Do the calculations.

$$t=\frac{8±10}{2}$$

Solve the equation t=\frac{8±10}{2} when ± is plus and when ± is minus.

$$t=9 t=-1$$

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

$$x=-3 x=3 x=-i x=i$$

Solve for x

$$x=-3$$

$$x=3$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-8t-9=0$$

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 -9 for c in the quadratic formula.

$$t=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 1\left(-9\right)}}{2}$$

Do the calculations.

$$t=\frac{8±10}{2}$$

Solve the equation t=\frac{8±10}{2} when ± is plus and when ± is minus.

$$t=9 t=-1$$

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

$$x=3 x=-3$$