Solve 5x^4-3x^2-2=0

$$5 x ^ { 4 } - 3 x ^ { 2 } - 2 = 0$$

Solve for x (complex solution)

$$x=1$$

$$x=-1$$

$$x=-\frac{\sqrt{10}i}{5}\approx -0-0.632455532i$$

$$x=\frac{\sqrt{10}i}{5}\approx 0.632455532i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$5t^{2}-3t-2=0$$

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 5 for a, -3 for b, and -2 for c in the quadratic formula.

$$t=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 5\left(-2\right)}}{2\times 5}$$

Do the calculations.

$$t=\frac{3±7}{10}$$

Solve the equation t=\frac{3±7}{10} when ± is plus and when ± is minus.

$$t=1 t=-\frac{2}{5}$$

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

$$x=-1 x=1 x=-\frac{\sqrt{10}i}{5} x=\frac{\sqrt{10}i}{5}$$

Solve for x

$$x=-1$$

$$x=1$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$5t^{2}-3t-2=0$$

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 5 for a, -3 for b, and -2 for c in the quadratic formula.

$$t=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 5\left(-2\right)}}{2\times 5}$$

Do the calculations.

$$t=\frac{3±7}{10}$$

Solve the equation t=\frac{3±7}{10} when ± is plus and when ± is minus.

$$t=1 t=-\frac{2}{5}$$

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

$$x=1 x=-1$$