Solve x^4-20x^2-125=0

$$x ^ { 4 } - 20 x ^ { 2 } - 125 = 0$$

Solve for x (complex solution)

$$x=5$$

$$x=-5$$

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

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

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-20t-125=0$$

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, -20 for b, and -125 for c in the quadratic formula.

$$t=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 1\left(-125\right)}}{2}$$

Do the calculations.

$$t=\frac{20±30}{2}$$

Solve the equation t=\frac{20±30}{2} when ± is plus and when ± is minus.

$$t=25 t=-5$$

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

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

Solve for x

$$x=-5$$

$$x=5$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-20t-125=0$$

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, -20 for b, and -125 for c in the quadratic formula.

$$t=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 1\left(-125\right)}}{2}$$

Do the calculations.

$$t=\frac{20±30}{2}$$

Solve the equation t=\frac{20±30}{2} when ± is plus and when ± is minus.

$$t=25 t=-5$$

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

$$x=5 x=-5$$