Solve 3x^4-37x^2+36=0

$$3 x ^ { 4 } - 37 x ^ { 2 } + 36 = 0$$

Solve for x

$$x = -\frac{\sqrt{222 - 6 \sqrt{937}}}{6} \approx -1.031951571$$

$$x = \frac{\sqrt{222 - 6 \sqrt{937}}}{6} \approx 1.031951571$$

$$x = \frac{\sqrt{6 \sqrt{937} + 222}}{6} \approx 3.356845139$$

$$x = -\frac{\sqrt{6 \sqrt{937} + 222}}{6} \approx -3.356845139$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$3t^{2}-37t+36=0$$

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 3 for a, -37 for b, and 36 for c in the quadratic formula.

$$t=\frac{-\left(-37\right)±\sqrt{\left(-37\right)^{2}-4\times 3\times 36}}{2\times 3}$$

Do the calculations.

$$t=\frac{37±\sqrt{937}}{6}$$

Solve the equation t=\frac{37±\sqrt{937}}{6} when ± is plus and when ± is minus.

$$t=\frac{\sqrt{937}+37}{6} t=\frac{37-\sqrt{937}}{6}$$

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

$$x=\frac{\sqrt{\frac{2\sqrt{937}+74}{3}}}{2} x=-\frac{\sqrt{\frac{2\sqrt{937}+74}{3}}}{2} x=\frac{\sqrt{\frac{74-2\sqrt{937}}{3}}}{2} x=-\frac{\sqrt{\frac{74-2\sqrt{937}}{3}}}{2}$$