Solve 26x^2+8x^4-20=6x^4+2x^2

$$26 x ^ { 2 } + 8 x ^ { 4 } - 20 = 6 x ^ { 4 } + 2 x ^ { 2 }$$

Solve for x (complex solution)

$$x=i\sqrt{\sqrt{46}+6}\approx 3.575238451i$$

$$x=-i\sqrt{\sqrt{46}+6}\approx -0-3.575238451i$$

$$x=-\sqrt{\sqrt{46}-6}\approx -0.884494196$$

$$x=\sqrt{\sqrt{46}-6}\approx 0.884494196$$

Steps Using the Quadratic Formula

Subtract 6x^{4} from both sides.

$$26x^{2}+8x^{4}-20-6x^{4}=2x^{2}$$

Combine 8x^{4} and -6x^{4} to get 2x^{4}.

$$26x^{2}+2x^{4}-20=2x^{2}$$

Subtract 2x^{2} from both sides.

$$26x^{2}+2x^{4}-20-2x^{2}=0$$

Combine 26x^{2} and -2x^{2} to get 24x^{2}.

$$24x^{2}+2x^{4}-20=0$$

Substitute t for x^{2}.

$$2t^{2}+24t-20=0$$

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, 24 for b, and -20 for c in the quadratic formula.

$$t=\frac{-24±\sqrt{24^{2}-4\times 2\left(-20\right)}}{2\times 2}$$

Do the calculations.

$$t=\frac{-24±4\sqrt{46}}{4}$$

Solve the equation t=\frac{-24±4\sqrt{46}}{4} when ± is plus and when ± is minus.

$$t=\sqrt{46}-6 t=-\sqrt{46}-6$$

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

$$x=-\sqrt{\sqrt{46}-6} x=\sqrt{\sqrt{46}-6} x=-i\sqrt{\sqrt{46}+6} x=i\sqrt{\sqrt{46}+6}$$

Solve for x

$$x=-\sqrt{\sqrt{46}-6}\approx -0.884494196$$

$$x=\sqrt{\sqrt{46}-6}\approx 0.884494196$$

Steps Using the Quadratic Formula

Subtract 6x^{4} from both sides.

$$26x^{2}+8x^{4}-20-6x^{4}=2x^{2}$$

Combine 8x^{4} and -6x^{4} to get 2x^{4}.

$$26x^{2}+2x^{4}-20=2x^{2}$$

Subtract 2x^{2} from both sides.

$$26x^{2}+2x^{4}-20-2x^{2}=0$$

Combine 26x^{2} and -2x^{2} to get 24x^{2}.

$$24x^{2}+2x^{4}-20=0$$

Substitute t for x^{2}.

$$2t^{2}+24t-20=0$$

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, 24 for b, and -20 for c in the quadratic formula.

$$t=\frac{-24±\sqrt{24^{2}-4\times 2\left(-20\right)}}{2\times 2}$$

Do the calculations.

$$t=\frac{-24±4\sqrt{46}}{4}$$

Solve the equation t=\frac{-24±4\sqrt{46}}{4} when ± is plus and when ± is minus.

$$t=\sqrt{46}-6 t=-\sqrt{46}-6$$

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

$$x=\sqrt{\sqrt{46}-6} x=-\sqrt{\sqrt{46}-6}$$