Solve -3x^4-4x^2+7=0

$$- 3 x ^ { 4 } - 4 x ^ { 2 } + 7 = 0$$

Solve for x (complex solution)

$$x=1$$

$$x=-1$$

$$x=-\frac{\sqrt{21}i}{3}\approx -0-1.527525232i$$

$$x=\frac{\sqrt{21}i}{3}\approx 1.527525232i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$-3t^{2}-4t+7=0$$

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 -3 for a, -4 for b, and 7 for c in the quadratic formula.

$$t=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-3\right)\times 7}}{-3\times 2}$$

Do the calculations.

$$t=\frac{4±10}{-6}$$

Solve the equation t=\frac{4±10}{-6} when ± is plus and when ± is minus.

$$t=-\frac{7}{3} t=1$$

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

$$x=-\frac{\sqrt{21}i}{3} x=\frac{\sqrt{21}i}{3} x=-1 x=1$$

Solve for x

$$x=-1$$

$$x=1$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$-3t^{2}-4t+7=0$$

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 -3 for a, -4 for b, and 7 for c in the quadratic formula.

$$t=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-3\right)\times 7}}{-3\times 2}$$

Do the calculations.

$$t=\frac{4±10}{-6}$$

Solve the equation t=\frac{4±10}{-6} when ± is plus and when ± is minus.

$$t=-\frac{7}{3} t=1$$

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

$$x=1 x=-1$$