Solve 9x^4+17x^2=2

$$9 x ^ { 4 } + 17 x ^ { 2 } = 2$$

Solve for x (complex solution)

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

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

$$x=-\sqrt{2}i\approx -0-1.414213562i$$

$$x=\sqrt{2}i\approx 1.414213562i$$

Steps Using the Quadratic Formula

Subtract 2 from both sides.

$$9x^{4}+17x^{2}-2=0$$

Substitute t for x^{2}.

$$9t^{2}+17t-2=0$$

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 9 for a, 17 for b, and -2 for c in the quadratic formula.

$$t=\frac{-17±\sqrt{17^{2}-4\times 9\left(-2\right)}}{2\times 9}$$

Do the calculations.

$$t=\frac{-17±19}{18}$$

Solve the equation t=\frac{-17±19}{18} when ± is plus and when ± is minus.

$$t=\frac{1}{9} t=-2$$

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

$$x=-\frac{1}{3} x=\frac{1}{3} x=-\sqrt{2}i x=\sqrt{2}i$$

Solve for x

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

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

Steps Using the Quadratic Formula

Subtract 2 from both sides.

$$9x^{4}+17x^{2}-2=0$$

Substitute t for x^{2}.

$$9t^{2}+17t-2=0$$

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 9 for a, 17 for b, and -2 for c in the quadratic formula.

$$t=\frac{-17±\sqrt{17^{2}-4\times 9\left(-2\right)}}{2\times 9}$$

Do the calculations.

$$t=\frac{-17±19}{18}$$

Solve the equation t=\frac{-17±19}{18} when ± is plus and when ± is minus.

$$t=\frac{1}{9} t=-2$$

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

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