Solve 9x^4+8x^2-1=0

$$9 x ^ { 4 } + 8 x ^ { 2 } - 1 = 0$$

Solve for x (complex solution)

$$x=\frac{1}{3}\approx 0.333333333$$

$$x=-\frac{1}{3}\approx -0.333333333$$

$$x=-i$$

$$x=i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$9t^{2}+8t-1=0$$

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 9 for a, 8 for b, and -1 for c in the quadratic formula.

$$t=\frac{-8±\sqrt{8^{2}-4\times 9\left(-1\right)}}{2\times 9}$$

Do the calculations.

$$t=\frac{-8±10}{18}$$

Solve the equation t=\frac{-8±10}{18} when ± is plus and when ± is minus.

$$t=\frac{1}{9} t=-1$$

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

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

Solve for x

$$x=-\frac{1}{3}\approx -0.333333333$$

$$x=\frac{1}{3}\approx 0.333333333$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$9t^{2}+8t-1=0$$

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 9 for a, 8 for b, and -1 for c in the quadratic formula.

$$t=\frac{-8±\sqrt{8^{2}-4\times 9\left(-1\right)}}{2\times 9}$$

Do the calculations.

$$t=\frac{-8±10}{18}$$

Solve the equation t=\frac{-8±10}{18} when ± is plus and when ± is minus.

$$t=\frac{1}{9} t=-1$$

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

$$x=\frac{1}{3} x=-\frac{1}{3}$$