Solve x^4+5x^2=-4

$$x ^ { 4 } + 5 x ^ { 2 } = - 4$$

Solve for x (complex solution)

$$x=i$$

$$x=-i$$

$$x=-2i$$

$$x=2i$$

Steps Using the Quadratic Formula

Add 4 to both sides.

$$x^{4}+5x^{2}+4=0$$

Substitute t for x^{2}.

$$t^{2}+5t+4=0$$

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, 5 for b, and 4 for c in the quadratic formula.

$$t=\frac{-5±\sqrt{5^{2}-4\times 1\times 4}}{2}$$

Do the calculations.

$$t=\frac{-5±3}{2}$$

Solve the equation t=\frac{-5±3}{2} when ± is plus and when ± is minus.

$$t=-1 t=-4$$

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

$$x=-i x=i x=-2i x=2i$$