Solve 81a^2=164

$$81 a ^ { 2 } = 164$$

Solve for a

$$a = \frac{2 \sqrt{41}}{9} \approx 1.422916497$$

$$a = -\frac{2 \sqrt{41}}{9} \approx -1.422916497$$

Steps by Finding Square Root

Divide both sides by 81.

$$a^{2}=\frac{164}{81}$$

Take the square root of both sides of the equation.

$$a=\frac{2\sqrt{41}}{9} a=-\frac{2\sqrt{41}}{9}$$

Steps Using the Quadratic Formula

Divide both sides by 81.

$$a^{2}=\frac{164}{81}$$

Subtract \frac{164}{81} from both sides.

$$a^{2}-\frac{164}{81}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{164}{81} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-\frac{164}{81}\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-\frac{164}{81}\right)}}{2}$$

Multiply -4 times -\frac{164}{81}.

$$a=\frac{0±\sqrt{\frac{656}{81}}}{2}$$

Take the square root of \frac{656}{81}.

$$a=\frac{0±\frac{4\sqrt{41}}{9}}{2}$$

Now solve the equation a=\frac{0±\frac{4\sqrt{41}}{9}}{2} when ± is plus.

$$a=\frac{2\sqrt{41}}{9}$$

Now solve the equation a=\frac{0±\frac{4\sqrt{41}}{9}}{2} when ± is minus.

$$a=-\frac{2\sqrt{41}}{9}$$

The equation is now solved.

$$a=\frac{2\sqrt{41}}{9} a=-\frac{2\sqrt{41}}{9}$$