Solve 12c^2-19=12

$$12 c ^ { 2 } - 19 = 12$$

Solve for c

$$c = \frac{\sqrt{93}}{6} \approx 1.607275127$$

$$c = -\frac{\sqrt{93}}{6} \approx -1.607275127$$

Steps by Finding Square Root

Add 19 to both sides.

$$12c^{2}=12+19$$

Add 12 and 19 to get 31.

$$12c^{2}=31$$

Divide both sides by 12.

$$c^{2}=\frac{31}{12}$$

Take the square root of both sides of the equation.

$$c=\frac{\sqrt{93}}{6} c=-\frac{\sqrt{93}}{6}$$

Steps Using the Quadratic Formula

Subtract 12 from both sides.

$$12c^{2}-19-12=0$$

Subtract 12 from -19 to get -31.

$$12c^{2}-31=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 12 for a, 0 for b, and -31 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\times 12\left(-31\right)}}{2\times 12}$$

Square 0.

$$c=\frac{0±\sqrt{-4\times 12\left(-31\right)}}{2\times 12}$$

Multiply -4 times 12.

$$c=\frac{0±\sqrt{-48\left(-31\right)}}{2\times 12}$$

Multiply -48 times -31.

$$c=\frac{0±\sqrt{1488}}{2\times 12}$$

Take the square root of 1488.

$$c=\frac{0±4\sqrt{93}}{2\times 12}$$

Multiply 2 times 12.

$$c=\frac{0±4\sqrt{93}}{24}$$

Now solve the equation c=\frac{0±4\sqrt{93}}{24} when ± is plus.

$$c=\frac{\sqrt{93}}{6}$$

Now solve the equation c=\frac{0±4\sqrt{93}}{24} when ± is minus.

$$c=-\frac{\sqrt{93}}{6}$$

The equation is now solved.

$$c=\frac{\sqrt{93}}{6} c=-\frac{\sqrt{93}}{6}$$