Solve 337a^2=254

$$337 a ^ { 2 } = 254$$

Solve for a

$$a=\frac{\sqrt{85598}}{337}\approx 0.868164269$$

$$a=-\frac{\sqrt{85598}}{337}\approx -0.868164269$$

Steps by Finding Square Root

Divide both sides by 337.

$$a^{2}=\frac{254}{337}$$

Take the square root of both sides of the equation.

$$a=\frac{\sqrt{85598}}{337} a=-\frac{\sqrt{85598}}{337}$$

Steps Using the Quadratic Formula

Divide both sides by 337.

$$a^{2}=\frac{254}{337}$$

Subtract \frac{254}{337} from both sides.

$$a^{2}-\frac{254}{337}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{254}{337} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-\frac{254}{337}\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-\frac{254}{337}\right)}}{2}$$

Multiply -4 times -\frac{254}{337}.

$$a=\frac{0±\sqrt{\frac{1016}{337}}}{2}$$

Take the square root of \frac{1016}{337}.

$$a=\frac{0±\frac{2\sqrt{85598}}{337}}{2}$$

Now solve the equation a=\frac{0±\frac{2\sqrt{85598}}{337}}{2} when ± is plus.

$$a=\frac{\sqrt{85598}}{337}$$

Now solve the equation a=\frac{0±\frac{2\sqrt{85598}}{337}}{2} when ± is minus.

$$a=-\frac{\sqrt{85598}}{337}$$

The equation is now solved.

$$a=\frac{\sqrt{85598}}{337} a=-\frac{\sqrt{85598}}{337}$$