Solve 6x^2+18=19

$$6 { x }^{ 2 } +18 = 19$$

Solve for x

$$x=\frac{\sqrt{6}}{6}\approx 0.40824829$$

$$x=-\frac{\sqrt{6}}{6}\approx -0.40824829$$

Steps by Finding Square Root

Subtract 18 from both sides.

$$6x^{2}=19-18$$

Subtract 18 from 19 to get 1.

$$6x^{2}=1$$

Divide both sides by 6.

$$x^{2}=\frac{1}{6}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{6}}{6} x=-\frac{\sqrt{6}}{6}$$

Steps Using the Quadratic Formula

Subtract 19 from both sides.

$$6x^{2}+18-19=0$$

Subtract 19 from 18 to get -1.

$$6x^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-1\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-1\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-1\right)}}{2\times 6}$$

Multiply -24 times -1.

$$x=\frac{0±\sqrt{24}}{2\times 6}$$

Take the square root of 24.

$$x=\frac{0±2\sqrt{6}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±2\sqrt{6}}{12}$$

Now solve the equation x=\frac{0±2\sqrt{6}}{12} when ± is plus.

$$x=\frac{\sqrt{6}}{6}$$

Now solve the equation x=\frac{0±2\sqrt{6}}{12} when ± is minus.

$$x=-\frac{\sqrt{6}}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{6}}{6} x=-\frac{\sqrt{6}}{6}$$