Solve 8-9m^2=m^4

$$8 - 9 m ^ { 2 } = m ^ { 4 }$$

Solve for m

$$m=-\frac{\sqrt{2\left(\sqrt{113}-9\right)}}{2}\approx -0.902813882$$

$$m=\frac{\sqrt{2\left(\sqrt{113}-9\right)}}{2}\approx 0.902813882$$

Steps Using the Quadratic Formula

Subtract m^{4} from both sides.

$$8-9m^{2}-m^{4}=0$$

Substitute t for m^{2}.

$$-t^{2}-9t+8=0$$

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, -9 for b, and 8 for c in the quadratic formula.

$$t=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\left(-1\right)\times 8}}{-2}$$

Do the calculations.

$$t=\frac{9±\sqrt{113}}{-2}$$

Solve the equation t=\frac{9±\sqrt{113}}{-2} when ± is plus and when ± is minus.

$$t=\frac{-\sqrt{113}-9}{2} t=\frac{\sqrt{113}-9}{2}$$

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

$$m=\frac{\sqrt{2\sqrt{113}-18}}{2} m=-\frac{\sqrt{2\sqrt{113}-18}}{2}$$