Solve 7x^4=-28x^2-21

$$7 x ^ { 4 } = - 28 x ^ { 2 } - 21$$

Solve for x (complex solution)

$$x=i$$

$$x=-i$$

$$x=-\sqrt{3}i\approx -0-1.732050808i$$

$$x=\sqrt{3}i\approx 1.732050808i$$

Steps Using the Quadratic Formula

Add 28x^{2} to both sides.

$$7x^{4}+28x^{2}=-21$$

Add 21 to both sides.

$$7x^{4}+28x^{2}+21=0$$

Substitute t for x^{2}.

$$7t^{2}+28t+21=0$$

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 7 for a, 28 for b, and 21 for c in the quadratic formula.

$$t=\frac{-28±\sqrt{28^{2}-4\times 7\times 21}}{2\times 7}$$

Do the calculations.

$$t=\frac{-28±14}{14}$$

Solve the equation t=\frac{-28±14}{14} when ± is plus and when ± is minus.

$$t=-1 t=-3$$

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

$$x=-i x=i x=-\sqrt{3}i x=\sqrt{3}i$$