Solve x^4+10x^2-75=0

$$x ^ { 4 } + 10 x ^ { 2 } - 75 = 0$$

Solve for x (complex solution)

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

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

$$x=-\sqrt{15}i\approx -0-3.872983346i$$

$$x=\sqrt{15}i\approx 3.872983346i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}+10t-75=0$$

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, 10 for b, and -75 for c in the quadratic formula.

$$t=\frac{-10±\sqrt{10^{2}-4\times 1\left(-75\right)}}{2}$$

Do the calculations.

$$t=\frac{-10±20}{2}$$

Solve the equation t=\frac{-10±20}{2} when ± is plus and when ± is minus.

$$t=5 t=-15$$

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

$$x=-\sqrt{5} x=\sqrt{5} x=-\sqrt{15}i x=\sqrt{15}i$$

Solve for x

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

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

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}+10t-75=0$$

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, 10 for b, and -75 for c in the quadratic formula.

$$t=\frac{-10±\sqrt{10^{2}-4\times 1\left(-75\right)}}{2}$$

Do the calculations.

$$t=\frac{-10±20}{2}$$

Solve the equation t=\frac{-10±20}{2} when ± is plus and when ± is minus.

$$t=5 t=-15$$

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

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