Solve 36x^4+30x^2=531

$$36 x ^ { 4 } + 30 x ^ { 2 } = 531$$

Solve for x (complex solution)

$$x=\frac{i\sqrt{3\left(\sqrt{2149}+5\right)}}{6}\approx 2.068761867i$$

$$x=-\frac{i\sqrt{3\left(\sqrt{2149}+5\right)}}{6}\approx -0-2.068761867i$$

$$x = -\frac{\sqrt{3 {(\sqrt{2149} - 5)}}}{6} \approx -1.856459622$$

$$x = \frac{\sqrt{3 {(\sqrt{2149} - 5)}}}{6} \approx 1.856459622$$

Steps Using the Quadratic Formula

Subtract 531 from both sides.

$$36x^{4}+30x^{2}-531=0$$

Substitute t for x^{2}.

$$36t^{2}+30t-531=0$$

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 36 for a, 30 for b, and -531 for c in the quadratic formula.

$$t=\frac{-30±\sqrt{30^{2}-4\times 36\left(-531\right)}}{2\times 36}$$

Do the calculations.

$$t=\frac{-30±6\sqrt{2149}}{72}$$

Solve the equation t=\frac{-30±6\sqrt{2149}}{72} when ± is plus and when ± is minus.

$$t=\frac{\sqrt{2149}-5}{12} t=\frac{-\sqrt{2149}-5}{12}$$

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

$$x=-\sqrt{\frac{\sqrt{2149}-5}{12}} x=\sqrt{\frac{\sqrt{2149}-5}{12}} x=-i\sqrt{\frac{\sqrt{2149}+5}{12}} x=i\sqrt{\frac{\sqrt{2149}+5}{12}}$$

Solve for x

$$x = -\frac{\sqrt{3 {(\sqrt{2149} - 5)}}}{6} \approx -1.856459622$$

$$x = \frac{\sqrt{3 {(\sqrt{2149} - 5)}}}{6} \approx 1.856459622$$

Steps Using the Quadratic Formula

Subtract 531 from both sides.

$$36x^{4}+30x^{2}-531=0$$

Substitute t for x^{2}.

$$36t^{2}+30t-531=0$$

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 36 for a, 30 for b, and -531 for c in the quadratic formula.

$$t=\frac{-30±\sqrt{30^{2}-4\times 36\left(-531\right)}}{2\times 36}$$

Do the calculations.

$$t=\frac{-30±6\sqrt{2149}}{72}$$

Solve the equation t=\frac{-30±6\sqrt{2149}}{72} when ± is plus and when ± is minus.

$$t=\frac{\sqrt{2149}-5}{12} t=\frac{-\sqrt{2149}-5}{12}$$

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

$$x=\frac{\sqrt{\frac{\sqrt{2149}-5}{3}}}{2} x=-\frac{\sqrt{\frac{\sqrt{2149}-5}{3}}}{2}$$