Solve x^4+6x^2=55

$$x ^ { 4 } + 6 x ^ { 2 } = 55$$

Solve for x (complex solution)

$$x=\sqrt{5}\approx 2.236067977$$

$$x=-\sqrt{5}\approx -2.236067977$$

$$x=-\sqrt{11}i\approx -0-3.31662479i$$

$$x=\sqrt{11}i\approx 3.31662479i$$

Steps Using the Quadratic Formula

Subtract 55 from both sides.

$$x^{4}+6x^{2}-55=0$$

Substitute t for x^{2}.

$$t^{2}+6t-55=0$$

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 1 for a, 6 for b, and -55 for c in the quadratic formula.

$$t=\frac{-6±\sqrt{6^{2}-4\times 1\left(-55\right)}}{2}$$

Do the calculations.

$$t=\frac{-6±16}{2}$$

Solve the equation t=\frac{-6±16}{2} when ± is plus and when ± is minus.

$$t=5 t=-11$$

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

$$x=-\sqrt{5} x=\sqrt{5} x=-\sqrt{11}i x=\sqrt{11}i$$

Solve for x

$$x=-\sqrt{5}\approx -2.236067977$$

$$x=\sqrt{5}\approx 2.236067977$$

Steps Using the Quadratic Formula

Subtract 55 from both sides.

$$x^{4}+6x^{2}-55=0$$

Substitute t for x^{2}.

$$t^{2}+6t-55=0$$

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 1 for a, 6 for b, and -55 for c in the quadratic formula.

$$t=\frac{-6±\sqrt{6^{2}-4\times 1\left(-55\right)}}{2}$$

Do the calculations.

$$t=\frac{-6±16}{2}$$

Solve the equation t=\frac{-6±16}{2} when ± is plus and when ± is minus.

$$t=5 t=-11$$

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

$$x=\sqrt{5} x=-\sqrt{5}$$