Solve 75x^4+73x^2+16=0

$$75 x ^ { 4 } + 73 x ^ { 2 } + 16 = 0$$

Solve for x (complex solution)

$$x=\frac{\sqrt{3}i}{3}\approx 0.577350269i$$

$$x=-\frac{\sqrt{3}i}{3}\approx -0-0.577350269i$$

$$x=-\frac{4}{5}i=-0.8i$$

$$x=\frac{4}{5}i=0.8i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$75t^{2}+73t+16=0$$

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 75 for a, 73 for b, and 16 for c in the quadratic formula.

$$t=\frac{-73±\sqrt{73^{2}-4\times 75\times 16}}{2\times 75}$$

Do the calculations.

$$t=\frac{-73±23}{150}$$

Solve the equation t=\frac{-73±23}{150} when ± is plus and when ± is minus.

$$t=-\frac{1}{3} t=-\frac{16}{25}$$

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

$$x=-\frac{\sqrt{3}i}{3} x=\frac{\sqrt{3}i}{3} x=-\frac{4}{5}i x=\frac{4}{5}i$$