Solve 16x^4+2x^2-5=0

$$16 x ^ { 4 } + 2 x ^ { 2 } - 5 = 0$$

Solve for x (complex solution)

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

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

$$x=-\frac{\sqrt{10}i}{4}\approx -0-0.790569415i$$

$$x=\frac{\sqrt{10}i}{4}\approx 0.790569415i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$16t^{2}+2t-5=0$$

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 16 for a, 2 for b, and -5 for c in the quadratic formula.

$$t=\frac{-2±\sqrt{2^{2}-4\times 16\left(-5\right)}}{2\times 16}$$

Do the calculations.

$$t=\frac{-2±18}{32}$$

Solve the equation t=\frac{-2±18}{32} when ± is plus and when ± is minus.

$$t=\frac{1}{2} t=-\frac{5}{8}$$

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

$$x=-\frac{\sqrt{2}}{2} x=\frac{\sqrt{2}}{2} x=-\frac{\sqrt{10}i}{4} x=\frac{\sqrt{10}i}{4}$$

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}.

$$16t^{2}+2t-5=0$$

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 16 for a, 2 for b, and -5 for c in the quadratic formula.

$$t=\frac{-2±\sqrt{2^{2}-4\times 16\left(-5\right)}}{2\times 16}$$

Do the calculations.

$$t=\frac{-2±18}{32}$$

Solve the equation t=\frac{-2±18}{32} when ± is plus and when ± is minus.

$$t=\frac{1}{2} t=-\frac{5}{8}$$

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

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