Solve 4x^4+3x^2-1=0

$$4 x ^ { 4 } + 3 x ^ { 2 } - 1 = 0$$

Solve for x (complex solution)

$$x=\frac{1}{2}=0.5$$

$$x=-\frac{1}{2}=-0.5$$

$$x=-i$$

$$x=i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$4t^{2}+3t-1=0$$

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 4 for a, 3 for b, and -1 for c in the quadratic formula.

$$t=\frac{-3±\sqrt{3^{2}-4\times 4\left(-1\right)}}{2\times 4}$$

Do the calculations.

$$t=\frac{-3±5}{8}$$

Solve the equation t=\frac{-3±5}{8} when ± is plus and when ± is minus.

$$t=\frac{1}{4} t=-1$$

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

$$x=-\frac{1}{2} x=\frac{1}{2} x=-i x=i$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

$$x=\frac{1}{2}=0.5$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$4t^{2}+3t-1=0$$

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 4 for a, 3 for b, and -1 for c in the quadratic formula.

$$t=\frac{-3±\sqrt{3^{2}-4\times 4\left(-1\right)}}{2\times 4}$$

Do the calculations.

$$t=\frac{-3±5}{8}$$

Solve the equation t=\frac{-3±5}{8} when ± is plus and when ± is minus.

$$t=\frac{1}{4} t=-1$$

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

$$x=\frac{1}{2} x=-\frac{1}{2}$$