Solve 3+12=1/2*98r^2

$$3 + 12 = \frac { 1 } { 2 } \times 98 r ^ { 2 }$$

Solve for r

$$r=\frac{\sqrt{15}}{7}\approx 0.553283335$$

$$r=-\frac{\sqrt{15}}{7}\approx -0.553283335$$

Steps by Finding Square Root

Add 3 and 12 to get 15.

$$15=\frac{1}{2}\times 98r^{2}$$

Multiply \frac{1}{2} and 98 to get 49.

$$15=49r^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$49r^{2}=15$$

Divide both sides by 49.

$$r^{2}=\frac{15}{49}$$

Take the square root of both sides of the equation.

$$r=\frac{\sqrt{15}}{7} r=-\frac{\sqrt{15}}{7}$$

Steps Using the Quadratic Formula

Add 3 and 12 to get 15.

$$15=\frac{1}{2}\times 98r^{2}$$

Multiply \frac{1}{2} and 98 to get 49.

$$15=49r^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$49r^{2}=15$$

Subtract 15 from both sides.

$$49r^{2}-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 49 for a, 0 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times 49\left(-15\right)}}{2\times 49}$$

Square 0.

$$r=\frac{0±\sqrt{-4\times 49\left(-15\right)}}{2\times 49}$$

Multiply -4 times 49.

$$r=\frac{0±\sqrt{-196\left(-15\right)}}{2\times 49}$$

Multiply -196 times -15.

$$r=\frac{0±\sqrt{2940}}{2\times 49}$$

Take the square root of 2940.

$$r=\frac{0±14\sqrt{15}}{2\times 49}$$

Multiply 2 times 49.

$$r=\frac{0±14\sqrt{15}}{98}$$

Now solve the equation r=\frac{0±14\sqrt{15}}{98} when ± is plus.

$$r=\frac{\sqrt{15}}{7}$$

Now solve the equation r=\frac{0±14\sqrt{15}}{98} when ± is minus.

$$r=-\frac{\sqrt{15}}{7}$$

The equation is now solved.

$$r=\frac{\sqrt{15}}{7} r=-\frac{\sqrt{15}}{7}$$