Solve 616=4*22/7*r^2

$$616 = 4 \times \frac { 22 } { 7 } \cdot r ^ { 2 }$$

Solve for r

$$r=7$$

$$r=-7$$

Steps Using Difference of Squares

Multiply 4 and \frac{22}{7} to get \frac{88}{7}.

$$616=\frac{88}{7}r^{2}$$

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

$$\frac{88}{7}r^{2}=616$$

Subtract 616 from both sides.

$$\frac{88}{7}r^{2}-616=0$$

Divide both sides by \frac{88}{7}.

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

Consider r^{2}-49. Rewrite r^{2}-49 as r^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(r-7\right)\left(r+7\right)=0$$

To find equation solutions, solve r-7=0 and r+7=0.

$$r=7 r=-7$$

Steps by Finding Square Root

Multiply 4 and \frac{22}{7} to get \frac{88}{7}.

$$616=\frac{88}{7}r^{2}$$

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

$$\frac{88}{7}r^{2}=616$$

Multiply both sides by \frac{7}{88}, the reciprocal of \frac{88}{7}.

$$r^{2}=616\times \frac{7}{88}$$

Multiply 616 and \frac{7}{88} to get 49.

$$r^{2}=49$$

Take the square root of both sides of the equation.

$$r=7 r=-7$$

Steps Using the Quadratic Formula

Multiply 4 and \frac{22}{7} to get \frac{88}{7}.

$$616=\frac{88}{7}r^{2}$$

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

$$\frac{88}{7}r^{2}=616$$

Subtract 616 from both sides.

$$\frac{88}{7}r^{2}-616=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{88}{7} for a, 0 for b, and -616 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times \frac{88}{7}\left(-616\right)}}{2\times \frac{88}{7}}$$

Square 0.

$$r=\frac{0±\sqrt{-4\times \frac{88}{7}\left(-616\right)}}{2\times \frac{88}{7}}$$

Multiply -4 times \frac{88}{7}.

$$r=\frac{0±\sqrt{-\frac{352}{7}\left(-616\right)}}{2\times \frac{88}{7}}$$

Multiply -\frac{352}{7} times -616.

$$r=\frac{0±\sqrt{30976}}{2\times \frac{88}{7}}$$

Take the square root of 30976.

$$r=\frac{0±176}{2\times \frac{88}{7}}$$

Multiply 2 times \frac{88}{7}.

$$r=\frac{0±176}{\frac{176}{7}}$$

Now solve the equation r=\frac{0±176}{\frac{176}{7}} when ± is plus. Divide 176 by \frac{176}{7} by multiplying 176 by the reciprocal of \frac{176}{7}.

$$r=7$$

Now solve the equation r=\frac{0±176}{\frac{176}{7}} when ± is minus. Divide -176 by \frac{176}{7} by multiplying -176 by the reciprocal of \frac{176}{7}.

$$r=-7$$

The equation is now solved.

$$r=7 r=-7$$