Solve 160x^4+358x^2-9=0

$$160 x ^ { 4 } + 358 x ^ { 2 } - 9 = 0$$

Solve for x (complex solution)

$$x=\frac{i\sqrt{10\left(\sqrt{33481}+179\right)}}{40}\approx 1.504115481i$$

$$x=-\frac{i\sqrt{10\left(\sqrt{33481}+179\right)}}{40}\approx -0-1.504115481i$$

$$x=-\frac{\sqrt{10\left(\sqrt{33481}-179\right)}}{40}\approx -0.15768126$$

$$x=\frac{\sqrt{10\left(\sqrt{33481}-179\right)}}{40}\approx 0.15768126$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$160t^{2}+358t-9=0$$

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 160 for a, 358 for b, and -9 for c in the quadratic formula.

$$t=\frac{-358±\sqrt{358^{2}-4\times 160\left(-9\right)}}{2\times 160}$$

Do the calculations.

$$t=\frac{-358±2\sqrt{33481}}{320}$$

Solve the equation t=\frac{-358±2\sqrt{33481}}{320} when ± is plus and when ± is minus.

$$t=\frac{\sqrt{33481}-179}{160} t=\frac{-\sqrt{33481}-179}{160}$$

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

$$x=-\sqrt{\frac{\sqrt{33481}-179}{160}} x=\sqrt{\frac{\sqrt{33481}-179}{160}} x=-i\sqrt{\frac{\sqrt{33481}+179}{160}} x=i\sqrt{\frac{\sqrt{33481}+179}{160}}$$

Solve for x

$$x=-\frac{\sqrt{10\left(\sqrt{33481}-179\right)}}{40}\approx -0.15768126$$

$$x=\frac{\sqrt{10\left(\sqrt{33481}-179\right)}}{40}\approx 0.15768126$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$160t^{2}+358t-9=0$$

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 160 for a, 358 for b, and -9 for c in the quadratic formula.

$$t=\frac{-358±\sqrt{358^{2}-4\times 160\left(-9\right)}}{2\times 160}$$

Do the calculations.

$$t=\frac{-358±2\sqrt{33481}}{320}$$

Solve the equation t=\frac{-358±2\sqrt{33481}}{320} when ± is plus and when ± is minus.

$$t=\frac{\sqrt{33481}-179}{160} t=\frac{-\sqrt{33481}-179}{160}$$

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

$$x=\frac{\sqrt{\frac{\sqrt{33481}-179}{40}}}{2} x=-\frac{\sqrt{\frac{\sqrt{33481}-179}{40}}}{2}$$