Solve x^4+7x^2+10=0

$${ x }^{ 4 } +7 { x }^{ 2 } +10=0$$

Solve for x (complex solution)

$$x=\sqrt{2}i\approx 1.414213562i$$

$$x=-\sqrt{2}i\approx -0-1.414213562i$$

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

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

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}+7t+10=0$$

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, 7 for b, and 10 for c in the quadratic formula.

$$t=\frac{-7±\sqrt{7^{2}-4\times 1\times 10}}{2}$$

Do the calculations.

$$t=\frac{-7±3}{2}$$

Solve the equation t=\frac{-7±3}{2} when ± is plus and when ± is minus.

$$t=-2 t=-5$$

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

$$x=-\sqrt{2}i x=\sqrt{2}i x=-\sqrt{5}i x=\sqrt{5}i$$