Solve 27=-x^4-12x^2

$$27 = - x ^ { 4 } - 12 x ^ { 2 }$$

Solve for x (complex solution)

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

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

$$x=-3i$$

$$x=3i$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$-x^{4}-12x^{2}=27$$

Subtract 27 from both sides.

$$-x^{4}-12x^{2}-27=0$$

Substitute t for x^{2}.

$$-t^{2}-12t-27=0$$

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, -12 for b, and -27 for c in the quadratic formula.

$$t=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\left(-1\right)\left(-27\right)}}{-2}$$

Do the calculations.

$$t=\frac{12±6}{-2}$$

Solve the equation t=\frac{12±6}{-2} when ± is plus and when ± is minus.

$$t=-9 t=-3$$

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

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