Solve x^4-2x^2=35

$$x ^ { 4 } - 2 x ^ { 2 } = 35$$

Solve for x (complex solution)

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

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

$$x=-\sqrt{5}i\approx -0-2.236067977i$$

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

Steps Using the Quadratic Formula

Subtract 35 from both sides.

$$x^{4}-2x^{2}-35=0$$

Substitute t for x^{2}.

$$t^{2}-2t-35=0$$

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, -2 for b, and -35 for c in the quadratic formula.

$$t=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 1\left(-35\right)}}{2}$$

Do the calculations.

$$t=\frac{2±12}{2}$$

Solve the equation t=\frac{2±12}{2} when ± is plus and when ± is minus.

$$t=7 t=-5$$

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

$$x=-\sqrt{7} x=\sqrt{7} x=-\sqrt{5}i x=\sqrt{5}i$$

Solve for x

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

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

Steps Using the Quadratic Formula

Subtract 35 from both sides.

$$x^{4}-2x^{2}-35=0$$

Substitute t for x^{2}.

$$t^{2}-2t-35=0$$

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, -2 for b, and -35 for c in the quadratic formula.

$$t=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 1\left(-35\right)}}{2}$$

Do the calculations.

$$t=\frac{2±12}{2}$$

Solve the equation t=\frac{2±12}{2} when ± is plus and when ± is minus.

$$t=7 t=-5$$

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

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