Solve 6x^2+18=49

$$6 x ^ { 2 } + 18 = 49$$

Solve for x

$$x = \frac{\sqrt{186}}{6} \approx 2.273030283$$

$$x = -\frac{\sqrt{186}}{6} \approx -2.273030283$$

Steps by Finding Square Root

Subtract 18 from both sides.

$$6x^{2}=49-18$$

Subtract 18 from 49 to get 31.

$$6x^{2}=31$$

Divide both sides by 6.

$$x^{2}=\frac{31}{6}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{186}}{6} x=-\frac{\sqrt{186}}{6}$$

Steps Using the Quadratic Formula

Subtract 49 from both sides.

$$6x^{2}+18-49=0$$

Subtract 49 from 18 to get -31.

$$6x^{2}-31=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -31 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-31\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-31\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-31\right)}}{2\times 6}$$

Multiply -24 times -31.

$$x=\frac{0±\sqrt{744}}{2\times 6}$$

Take the square root of 744.

$$x=\frac{0±2\sqrt{186}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±2\sqrt{186}}{12}$$

Now solve the equation x=\frac{0±2\sqrt{186}}{12} when ± is plus.

$$x=\frac{\sqrt{186}}{6}$$

Now solve the equation x=\frac{0±2\sqrt{186}}{12} when ± is minus.

$$x=-\frac{\sqrt{186}}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{186}}{6} x=-\frac{\sqrt{186}}{6}$$