Solve 2x^4+17x^2-9=0

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

Solve for x (complex solution)

$$x=\frac{\sqrt{2}}{2}\approx 0.707106781$$

$$x=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

$$x=-3i$$

$$x=3i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

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

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

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

Do the calculations.

$$t=\frac{-17±19}{4}$$

Solve the equation t=\frac{-17±19}{4} when ± is plus and when ± is minus.

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

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

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

Solve for x

$$x=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

$$x=\frac{\sqrt{2}}{2}\approx 0.707106781$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

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

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

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

Do the calculations.

$$t=\frac{-17±19}{4}$$

Solve the equation t=\frac{-17±19}{4} when ± is plus and when ± is minus.

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

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

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