Solve x^4+6x^2-91=0

$$x ^ { 4 } + 6 x ^ { 2 } - 91 = 0$$

Solve for x (complex solution)

$$x=\sqrt{7}\approx 2.645751311$$

$$x=-\sqrt{7}\approx -2.645751311$$

$$x=-\sqrt{13}i\approx -0-3.605551275i$$

$$x=\sqrt{13}i\approx 3.605551275i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}+6t-91=0$$

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, 6 for b, and -91 for c in the quadratic formula.

$$t=\frac{-6±\sqrt{6^{2}-4\times 1\left(-91\right)}}{2}$$

Do the calculations.

$$t=\frac{-6±20}{2}$$

Solve the equation t=\frac{-6±20}{2} when ± is plus and when ± is minus.

$$t=7 t=-13$$

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

$$x=-\sqrt{7} x=\sqrt{7} x=-\sqrt{13}i x=\sqrt{13}i$$

Solve for x

$$x=-\sqrt{7}\approx -2.645751311$$

$$x=\sqrt{7}\approx 2.645751311$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}+6t-91=0$$

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, 6 for b, and -91 for c in the quadratic formula.

$$t=\frac{-6±\sqrt{6^{2}-4\times 1\left(-91\right)}}{2}$$

Do the calculations.

$$t=\frac{-6±20}{2}$$

Solve the equation t=\frac{-6±20}{2} when ± is plus and when ± is minus.

$$t=7 t=-13$$

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

$$x=\sqrt{7} x=-\sqrt{7}$$