Solve 1232=1/3*22/7*r^2*24

$$1232 = \frac { 1 } { 3 } \times \frac { 22 } { 7 } \times r ^ { 2 } \times 24$$

Solve for r

$$r=7$$

$$r=-7$$

Steps Using Difference of Squares

Multiply \frac{1}{3} and \frac{22}{7} to get \frac{22}{21}.

$$1232=\frac{22}{21}r^{2}\times 24$$

Multiply \frac{22}{21} and 24 to get \frac{176}{7}.

$$1232=\frac{176}{7}r^{2}$$

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

$$\frac{176}{7}r^{2}=1232$$

Subtract 1232 from both sides.

$$\frac{176}{7}r^{2}-1232=0$$

Divide both sides by \frac{176}{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 \frac{1}{3} and \frac{22}{7} to get \frac{22}{21}.

$$1232=\frac{22}{21}r^{2}\times 24$$

Multiply \frac{22}{21} and 24 to get \frac{176}{7}.

$$1232=\frac{176}{7}r^{2}$$

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

$$\frac{176}{7}r^{2}=1232$$

Multiply both sides by \frac{7}{176}, the reciprocal of \frac{176}{7}.

$$r^{2}=1232\times \frac{7}{176}$$

Multiply 1232 and \frac{7}{176} 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 \frac{1}{3} and \frac{22}{7} to get \frac{22}{21}.

$$1232=\frac{22}{21}r^{2}\times 24$$

Multiply \frac{22}{21} and 24 to get \frac{176}{7}.

$$1232=\frac{176}{7}r^{2}$$

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

$$\frac{176}{7}r^{2}=1232$$

Subtract 1232 from both sides.

$$\frac{176}{7}r^{2}-1232=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{176}{7} for a, 0 for b, and -1232 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times \frac{176}{7}\left(-1232\right)}}{2\times \frac{176}{7}}$$

Square 0.

$$r=\frac{0±\sqrt{-4\times \frac{176}{7}\left(-1232\right)}}{2\times \frac{176}{7}}$$

Multiply -4 times \frac{176}{7}.

$$r=\frac{0±\sqrt{-\frac{704}{7}\left(-1232\right)}}{2\times \frac{176}{7}}$$

Multiply -\frac{704}{7} times -1232.

$$r=\frac{0±\sqrt{123904}}{2\times \frac{176}{7}}$$

Take the square root of 123904.

$$r=\frac{0±352}{2\times \frac{176}{7}}$$

Multiply 2 times \frac{176}{7}.

$$r=\frac{0±352}{\frac{352}{7}}$$

Now solve the equation r=\frac{0±352}{\frac{352}{7}} when ± is plus. Divide 352 by \frac{352}{7} by multiplying 352 by the reciprocal of \frac{352}{7}.

$$r=7$$

Now solve the equation r=\frac{0±352}{\frac{352}{7}} when ± is minus. Divide -352 by \frac{352}{7} by multiplying -352 by the reciprocal of \frac{352}{7}.

$$r=-7$$

The equation is now solved.

$$r=7 r=-7$$