Solve operatorname{ran}pi/4+(pi/2)^2+c=pi^2/4+9

$$\operatorname { ran } \frac { \pi } { 4 } + ( \frac { \pi } { 2 } ) ^ { 2 } + c = \frac { \pi ^ { 2 } } { 4 } + 9$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{4\left(c-9\right)}{\pi nr}\text{, }&n\neq 0\text{ and }r\neq 0\\a\in \mathrm{R}\text{, }&\left(r=0\text{ or }n=0\right)\text{ and }c=9\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$ran\pi +4\times \left(\frac{\pi }{2}\right)^{2}+4c=\pi ^{2}+36$$

To raise \frac{\pi }{2} to a power, raise both numerator and denominator to the power and then divide.

$$ran\pi +4\times \frac{\pi ^{2}}{2^{2}}+4c=\pi ^{2}+36$$

Express 4\times \frac{\pi ^{2}}{2^{2}} as a single fraction.

$$ran\pi +\frac{4\pi ^{2}}{2^{2}}+4c=\pi ^{2}+36$$

Calculate 2 to the power of 2 and get 4.

$$ran\pi +\frac{4\pi ^{2}}{4}+4c=\pi ^{2}+36$$

Cancel out 4 and 4.

$$ran\pi +\pi ^{2}+4c=\pi ^{2}+36$$

Subtract \pi ^{2} from both sides.

$$ran\pi +4c=\pi ^{2}+36-\pi ^{2}$$

Combine \pi ^{2} and -\pi ^{2} to get 0.

$$ran\pi +4c=36$$

Subtract 4c from both sides.

$$ran\pi =36-4c$$

The equation is in standard form.

$$\pi nra=36-4c$$

Divide both sides by rn\pi .

$$\frac{\pi nra}{\pi nr}=\frac{36-4c}{\pi nr}$$

Dividing by rn\pi undoes the multiplication by rn\pi .

$$a=\frac{36-4c}{\pi nr}$$

Divide 36-4c by rn\pi .

$$a=\frac{4\left(9-c\right)}{\pi nr}$$

Solve for c

$$c=-\frac{\pi anr}{4}+9$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$ran\pi +4\times \left(\frac{\pi }{2}\right)^{2}+4c=\pi ^{2}+36$$

To raise \frac{\pi }{2} to a power, raise both numerator and denominator to the power and then divide.

$$ran\pi +4\times \frac{\pi ^{2}}{2^{2}}+4c=\pi ^{2}+36$$

Express 4\times \frac{\pi ^{2}}{2^{2}} as a single fraction.

$$ran\pi +\frac{4\pi ^{2}}{2^{2}}+4c=\pi ^{2}+36$$

Calculate 2 to the power of 2 and get 4.

$$ran\pi +\frac{4\pi ^{2}}{4}+4c=\pi ^{2}+36$$

Cancel out 4 and 4.

$$ran\pi +\pi ^{2}+4c=\pi ^{2}+36$$

Subtract ran\pi from both sides.

$$\pi ^{2}+4c=\pi ^{2}+36-ran\pi$$

Subtract \pi ^{2} from both sides.

$$4c=\pi ^{2}+36-ran\pi -\pi ^{2}$$

Combine \pi ^{2} and -\pi ^{2} to get 0.

$$4c=36-ran\pi$$

The equation is in standard form.

$$4c=36-\pi anr$$

Divide both sides by 4.

$$\frac{4c}{4}=\frac{36-\pi anr}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$c=\frac{36-\pi anr}{4}$$

Divide 36-ran\pi by 4.

$$c=-\frac{\pi anr}{4}+9$$