Solve 2(r^2+3)=108

$$2 ( r ^ { 2 } + 3 ) = 108$$

Solve for r

$$r=\sqrt{51}\approx 7.141428429$$

$$r=-\sqrt{51}\approx -7.141428429$$

Steps by Finding Square Root

Divide both sides by 2.

$$r^{2}+3=\frac{108}{2}$$

Divide 108 by 2 to get 54.

$$r^{2}+3=54$$

Subtract 3 from both sides.

$$r^{2}=54-3$$

Subtract 3 from 54 to get 51.

$$r^{2}=51$$

Take the square root of both sides of the equation.

$$r=\sqrt{51} r=-\sqrt{51}$$

Steps Using the Quadratic Formula

Divide both sides by 2.

$$r^{2}+3=\frac{108}{2}$$

Divide 108 by 2 to get 54.

$$r^{2}+3=54$$

Subtract 54 from both sides.

$$r^{2}+3-54=0$$

Subtract 54 from 3 to get -51.

$$r^{2}-51=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -51 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-51\right)}}{2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-51\right)}}{2}$$

Multiply -4 times -51.

$$r=\frac{0±\sqrt{204}}{2}$$

Take the square root of 204.

$$r=\frac{0±2\sqrt{51}}{2}$$

Now solve the equation r=\frac{0±2\sqrt{51}}{2} when ± is plus.

$$r=\sqrt{51}$$

Now solve the equation r=\frac{0±2\sqrt{51}}{2} when ± is minus.

$$r=-\sqrt{51}$$

The equation is now solved.

$$r=\sqrt{51} r=-\sqrt{51}$$