Solve x^4-6x^2-7=0

$$x ^ { 4 } - 6 x ^ { 2 } - 7 = 0$$

Solve for x (complex solution)

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

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

$$x=-i$$

$$x=i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-6t-7=0$$

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 -7 for c in the quadratic formula.

$$t=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 1\left(-7\right)}}{2}$$

Do the calculations.

$$t=\frac{6±8}{2}$$

Solve the equation t=\frac{6±8}{2} when ± is plus and when ± is minus.

$$t=7 t=-1$$

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

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

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}.

$$t^{2}-6t-7=0$$

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 -7 for c in the quadratic formula.

$$t=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 1\left(-7\right)}}{2}$$

Do the calculations.

$$t=\frac{6±8}{2}$$

Solve the equation t=\frac{6±8}{2} when ± is plus and when ± is minus.

$$t=7 t=-1$$

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

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