Solve 8x^2+5x^4-13=0

$$8 x ^ { 2 } + 5 x ^ { 4 } - 13 = 0$$

Solve for x (complex solution)

$$x=1$$

$$x=-1$$

$$x=-\frac{\sqrt{65}i}{5}\approx -0-1.61245155i$$

$$x=\frac{\sqrt{65}i}{5}\approx 1.61245155i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$5t^{2}+8t-13=0$$

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 5 for a, 8 for b, and -13 for c in the quadratic formula.

$$t=\frac{-8±\sqrt{8^{2}-4\times 5\left(-13\right)}}{2\times 5}$$

Do the calculations.

$$t=\frac{-8±18}{10}$$

Solve the equation t=\frac{-8±18}{10} when ± is plus and when ± is minus.

$$t=1 t=-\frac{13}{5}$$

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

$$x=-1 x=1 x=-\frac{\sqrt{65}i}{5} x=\frac{\sqrt{65}i}{5}$$

Solve for x

$$x=-1$$

$$x=1$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$5t^{2}+8t-13=0$$

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 5 for a, 8 for b, and -13 for c in the quadratic formula.

$$t=\frac{-8±\sqrt{8^{2}-4\times 5\left(-13\right)}}{2\times 5}$$

Do the calculations.

$$t=\frac{-8±18}{10}$$

Solve the equation t=\frac{-8±18}{10} when ± is plus and when ± is minus.

$$t=1 t=-\frac{13}{5}$$

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

$$x=1 x=-1$$