Solve 22/7*R^2=314.28

$$\frac { 22 } { 7 } \times R ^ { 2 } = 314.28$$

Solve for R

$$R = \frac{9 \sqrt{14938}}{110} \approx 9.99990909$$

$$R = -\frac{9 \sqrt{14938}}{110} \approx -9.99990909$$

Steps by Finding Square Root

Multiply both sides by \frac{7}{22}, the reciprocal of \frac{22}{7}.

$$R^{2}=314.28\times \frac{7}{22}$$

Multiply 314.28 and \frac{7}{22} to get \frac{54999}{550}.

$$R^{2}=\frac{54999}{550}$$

Take the square root of both sides of the equation.

$$R=\frac{9\sqrt{14938}}{110} R=-\frac{9\sqrt{14938}}{110}$$

Steps Using the Quadratic Formula

Multiply both sides by \frac{7}{22}, the reciprocal of \frac{22}{7}.

$$R^{2}=314.28\times \frac{7}{22}$$

Multiply 314.28 and \frac{7}{22} to get \frac{54999}{550}.

$$R^{2}=\frac{54999}{550}$$

Subtract \frac{54999}{550} from both sides.

$$R^{2}-\frac{54999}{550}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{54999}{550} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$R=\frac{0±\sqrt{0^{2}-4\left(-\frac{54999}{550}\right)}}{2}$$

Square 0.

$$R=\frac{0±\sqrt{-4\left(-\frac{54999}{550}\right)}}{2}$$

Multiply -4 times -\frac{54999}{550}.

$$R=\frac{0±\sqrt{\frac{109998}{275}}}{2}$$

Take the square root of \frac{109998}{275}.

$$R=\frac{0±\frac{9\sqrt{14938}}{55}}{2}$$

Now solve the equation R=\frac{0±\frac{9\sqrt{14938}}{55}}{2} when ± is plus.

$$R=\frac{9\sqrt{14938}}{110}$$

Now solve the equation R=\frac{0±\frac{9\sqrt{14938}}{55}}{2} when ± is minus.

$$R=-\frac{9\sqrt{14938}}{110}$$

The equation is now solved.

$$R=\frac{9\sqrt{14938}}{110} R=-\frac{9\sqrt{14938}}{110}$$