Solve 9a^4-37a^2+4=0

$$9 a ^ { 4 } - 37 a ^ { 2 } + 4 = 0$$

Solve for a

$$a=-2$$

$$a=2$$

$$a=\frac{1}{3}\approx 0.333333333$$

$$a=-\frac{1}{3}\approx -0.333333333$$

Steps Using the Quadratic Formula

Substitute t for a^{2}.

$$9t^{2}-37t+4=0$$

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 9 for a, -37 for b, and 4 for c in the quadratic formula.

$$t=\frac{-\left(-37\right)±\sqrt{\left(-37\right)^{2}-4\times 9\times 4}}{2\times 9}$$

Do the calculations.

$$t=\frac{37±35}{18}$$

Solve the equation t=\frac{37±35}{18} when ± is plus and when ± is minus.

$$t=4 t=\frac{1}{9}$$

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

$$a=2 a=-2 a=\frac{1}{3} a=-\frac{1}{3}$$