Solve 27m^4-30m^2+7=0

$$27 m ^ { 4 } - 30 m ^ { 2 } + 7 = 0$$

Solve for m

$$m=-\frac{\sqrt{7}}{3}\approx -0.881917104$$

$$m=\frac{\sqrt{7}}{3}\approx 0.881917104$$

$$m=\frac{\sqrt{3}}{3}\approx 0.577350269$$

$$m=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

Steps Using the Quadratic Formula

Substitute t for m^{2}.

$$27t^{2}-30t+7=0$$

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 27 for a, -30 for b, and 7 for c in the quadratic formula.

$$t=\frac{-\left(-30\right)±\sqrt{\left(-30\right)^{2}-4\times 27\times 7}}{2\times 27}$$

Do the calculations.

$$t=\frac{30±12}{54}$$

Solve the equation t=\frac{30±12}{54} when ± is plus and when ± is minus.

$$t=\frac{7}{9} t=\frac{1}{3}$$

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

$$m=\frac{\sqrt{7}}{3} m=-\frac{\sqrt{7}}{3} m=\frac{\sqrt{3}}{3} m=-\frac{\sqrt{3}}{3}$$