Solve 0=x^4-5x^2-44

$$0 = { x }^{ 4 } -5 { x }^{ 2 } -44$$

Solve for x (complex solution)

$$x=\frac{i\sqrt{2\left(\sqrt{201}-5\right)}}{2}\approx 2.142130584i$$

$$x=-\frac{i\sqrt{2\left(\sqrt{201}-5\right)}}{2}\approx -0-2.142130584i$$

$$x = -\frac{\sqrt{2 {(\sqrt{201} + 5)}}}{2} \approx -3.096566395$$

$$x = \frac{\sqrt{2 {(\sqrt{201} + 5)}}}{2} \approx 3.096566395$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$x^{4}-5x^{2}-44=0$$

Substitute t for x^{2}.

$$t^{2}-5t-44=0$$

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, -5 for b, and -44 for c in the quadratic formula.

$$t=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 1\left(-44\right)}}{2}$$

Do the calculations.

$$t=\frac{5±\sqrt{201}}{2}$$

Solve the equation t=\frac{5±\sqrt{201}}{2} when ± is plus and when ± is minus.

$$t=\frac{\sqrt{201}+5}{2} t=\frac{5-\sqrt{201}}{2}$$

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

$$x=-\sqrt{\frac{\sqrt{201}+5}{2}} x=\sqrt{\frac{\sqrt{201}+5}{2}} x=-i\sqrt{-\frac{5-\sqrt{201}}{2}} x=i\sqrt{-\frac{5-\sqrt{201}}{2}}$$

Solve for x

$$x = -\frac{\sqrt{2 {(\sqrt{201} + 5)}}}{2} \approx -3.096566395$$

$$x = \frac{\sqrt{2 {(\sqrt{201} + 5)}}}{2} \approx 3.096566395$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$x^{4}-5x^{2}-44=0$$

Substitute t for x^{2}.

$$t^{2}-5t-44=0$$

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, -5 for b, and -44 for c in the quadratic formula.

$$t=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 1\left(-44\right)}}{2}$$

Do the calculations.

$$t=\frac{5±\sqrt{201}}{2}$$

Solve the equation t=\frac{5±\sqrt{201}}{2} when ± is plus and when ± is minus.

$$t=\frac{\sqrt{201}+5}{2} t=\frac{5-\sqrt{201}}{2}$$

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

$$x=\frac{\sqrt{2\sqrt{201}+10}}{2} x=-\frac{\sqrt{2\sqrt{201}+10}}{2}$$