Solve 19a^2=9

$$19 a ^ { 2 } = 9$$

Solve for a

$$a=\frac{3\sqrt{19}}{19}\approx 0.688247202$$

$$a=-\frac{3\sqrt{19}}{19}\approx -0.688247202$$

Steps by Finding Square Root

Divide both sides by 19.

$$a^{2}=\frac{9}{19}$$

Take the square root of both sides of the equation.

$$a=\frac{3\sqrt{19}}{19} a=-\frac{3\sqrt{19}}{19}$$

Steps Using the Quadratic Formula

Divide both sides by 19.

$$a^{2}=\frac{9}{19}$$

Subtract \frac{9}{19} from both sides.

$$a^{2}-\frac{9}{19}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{9}{19} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-\frac{9}{19}\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-\frac{9}{19}\right)}}{2}$$

Multiply -4 times -\frac{9}{19}.

$$a=\frac{0±\sqrt{\frac{36}{19}}}{2}$$

Take the square root of \frac{36}{19}.

$$a=\frac{0±\frac{6\sqrt{19}}{19}}{2}$$

Now solve the equation a=\frac{0±\frac{6\sqrt{19}}{19}}{2} when ± is plus.

$$a=\frac{3\sqrt{19}}{19}$$

Now solve the equation a=\frac{0±\frac{6\sqrt{19}}{19}}{2} when ± is minus.

$$a=-\frac{3\sqrt{19}}{19}$$

The equation is now solved.

$$a=\frac{3\sqrt{19}}{19} a=-\frac{3\sqrt{19}}{19}$$