Solve 9x^4+6x^2-8=0

$$9 x ^ { 4 } + 6 x ^ { 2 } - 8 = 0$$

Solve for x (complex solution)

$$x=\frac{\sqrt{6}}{3}\approx 0.816496581$$

$$x=-\frac{\sqrt{6}}{3}\approx -0.816496581$$

$$x=-\frac{2\sqrt{3}i}{3}\approx -0-1.154700538i$$

$$x=\frac{2\sqrt{3}i}{3}\approx 1.154700538i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$9t^{2}+6t-8=0$$

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, 6 for b, and -8 for c in the quadratic formula.

$$t=\frac{-6±\sqrt{6^{2}-4\times 9\left(-8\right)}}{2\times 9}$$

Do the calculations.

$$t=\frac{-6±18}{18}$$

Solve the equation t=\frac{-6±18}{18} when ± is plus and when ± is minus.

$$t=\frac{2}{3} t=-\frac{4}{3}$$

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

$$x=-\frac{\sqrt{6}}{3} x=\frac{\sqrt{6}}{3} x=-\frac{2\sqrt{3}i}{3} x=\frac{2\sqrt{3}i}{3}$$

Solve for x

$$x=-\frac{\sqrt{6}}{3}\approx -0.816496581$$

$$x=\frac{\sqrt{6}}{3}\approx 0.816496581$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$9t^{2}+6t-8=0$$

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, 6 for b, and -8 for c in the quadratic formula.

$$t=\frac{-6±\sqrt{6^{2}-4\times 9\left(-8\right)}}{2\times 9}$$

Do the calculations.

$$t=\frac{-6±18}{18}$$

Solve the equation t=\frac{-6±18}{18} when ± is plus and when ± is minus.

$$t=\frac{2}{3} t=-\frac{4}{3}$$

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

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$