Solve S={6*7^2+2*22/7*(7/2)^2-22/7*(7/2)^2}cm^2

$$S = \{ 6 \times 7 ^ { 2 } + 2 \times \frac { 22 } { 7 } \times ( \frac { 7 } { 2 } ) ^ { 2 } - \frac { 22 } { 7 } \times ( \frac { 7 } { 2 } ) ^ { 2 } \} cm ^ { 2 }$$

Solve for S

$$S=\frac{665cm^{2}}{2}$$

Solution Steps

Calculate 7 to the power of 2 and get 49.

$$S=\left(6\times 49+2\times \frac{22}{7}\times \left(\frac{7}{2}\right)^{2}-\frac{22}{7}\times \left(\frac{7}{2}\right)^{2}\right)cm^{2}$$

Multiply 6 and 49 to get 294.

$$S=\left(294+2\times \frac{22}{7}\times \left(\frac{7}{2}\right)^{2}-\frac{22}{7}\times \left(\frac{7}{2}\right)^{2}\right)cm^{2}$$

Multiply 2 and \frac{22}{7} to get \frac{44}{7}.

$$S=\left(294+\frac{44}{7}\times \left(\frac{7}{2}\right)^{2}-\frac{22}{7}\times \left(\frac{7}{2}\right)^{2}\right)cm^{2}$$

Calculate \frac{7}{2} to the power of 2 and get \frac{49}{4}.

$$S=\left(294+\frac{44}{7}\times \frac{49}{4}-\frac{22}{7}\times \left(\frac{7}{2}\right)^{2}\right)cm^{2}$$

Multiply \frac{44}{7} and \frac{49}{4} to get 77.

$$S=\left(294+77-\frac{22}{7}\times \left(\frac{7}{2}\right)^{2}\right)cm^{2}$$

Add 294 and 77 to get 371.

$$S=\left(371-\frac{22}{7}\times \left(\frac{7}{2}\right)^{2}\right)cm^{2}$$

Calculate \frac{7}{2} to the power of 2 and get \frac{49}{4}.

$$S=\left(371-\frac{22}{7}\times \frac{49}{4}\right)cm^{2}$$

Multiply \frac{22}{7} and \frac{49}{4} to get \frac{77}{2}.

$$S=\left(371-\frac{77}{2}\right)cm^{2}$$

Subtract \frac{77}{2} from 371 to get \frac{665}{2}.

$$S=\frac{665}{2}cm^{2}$$

Solve for c

$$\left\{\begin{matrix}c=\frac{2S}{665m^{2}}\text{, }&m\neq 0\\c\in \mathrm{R}\text{, }&S=0\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 7 to the power of 2 and get 49.

$$S=\left(6\times 49+2\times \frac{22}{7}\times \left(\frac{7}{2}\right)^{2}-\frac{22}{7}\times \left(\frac{7}{2}\right)^{2}\right)cm^{2}$$

Multiply 6 and 49 to get 294.

$$S=\left(294+2\times \frac{22}{7}\times \left(\frac{7}{2}\right)^{2}-\frac{22}{7}\times \left(\frac{7}{2}\right)^{2}\right)cm^{2}$$

Multiply 2 and \frac{22}{7} to get \frac{44}{7}.

$$S=\left(294+\frac{44}{7}\times \left(\frac{7}{2}\right)^{2}-\frac{22}{7}\times \left(\frac{7}{2}\right)^{2}\right)cm^{2}$$

Calculate \frac{7}{2} to the power of 2 and get \frac{49}{4}.

$$S=\left(294+\frac{44}{7}\times \frac{49}{4}-\frac{22}{7}\times \left(\frac{7}{2}\right)^{2}\right)cm^{2}$$

Multiply \frac{44}{7} and \frac{49}{4} to get 77.

$$S=\left(294+77-\frac{22}{7}\times \left(\frac{7}{2}\right)^{2}\right)cm^{2}$$

Add 294 and 77 to get 371.

$$S=\left(371-\frac{22}{7}\times \left(\frac{7}{2}\right)^{2}\right)cm^{2}$$

Calculate \frac{7}{2} to the power of 2 and get \frac{49}{4}.

$$S=\left(371-\frac{22}{7}\times \frac{49}{4}\right)cm^{2}$$

Multiply \frac{22}{7} and \frac{49}{4} to get \frac{77}{2}.

$$S=\left(371-\frac{77}{2}\right)cm^{2}$$

Subtract \frac{77}{2} from 371 to get \frac{665}{2}.

$$S=\frac{665}{2}cm^{2}$$

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

$$\frac{665}{2}cm^{2}=S$$

The equation is in standard form.

$$\frac{665m^{2}}{2}c=S$$

Divide both sides by \frac{665}{2}m^{2}.

$$\frac{2\times \frac{665m^{2}}{2}c}{665m^{2}}=\frac{2S}{665m^{2}}$$

Dividing by \frac{665}{2}m^{2} undoes the multiplication by \frac{665}{2}m^{2}.

$$c=\frac{2S}{665m^{2}}$$