Solve 7000cm^2=1/2left(a+117cmright)4+cm

$$7000c { m }^{ 2 } = \frac{ 1 }{ 2 } \left( a+117cm \right) 4+cm$$

Solve for a

$$a=-\frac{5cm\left(47-1400m\right)}{2}$$

Steps for Solving Linear Equation

Multiply \frac{1}{2} and 4 to get 2.

$$7000cm^{2}=2\left(a+117cm\right)+cm$$

Use the distributive property to multiply 2 by a+117cm.

$$7000cm^{2}=2a+234cm+cm$$

Combine 234cm and cm to get 235cm.

$$7000cm^{2}=2a+235cm$$

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

$$2a+235cm=7000cm^{2}$$

Subtract 235cm from both sides.

$$2a=7000cm^{2}-235cm$$

Divide both sides by 2.

$$\frac{2a}{2}=\frac{5cm\left(1400m-47\right)}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$a=\frac{5cm\left(1400m-47\right)}{2}$$

Solve for c

$$\left\{\begin{matrix}c=\frac{2a}{5m\left(1400m-47\right)}\text{, }&m\neq \frac{47}{1400}\text{ and }m\neq 0\\c\in \mathrm{R}\text{, }&\left(m=0\text{ or }m=\frac{47}{1400}\right)\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply \frac{1}{2} and 4 to get 2.

$$7000cm^{2}=2\left(a+117cm\right)+cm$$

Use the distributive property to multiply 2 by a+117cm.

$$7000cm^{2}=2a+234cm+cm$$

Combine 234cm and cm to get 235cm.

$$7000cm^{2}=2a+235cm$$

Subtract 235cm from both sides.

$$7000cm^{2}-235cm=2a$$

Combine all terms containing c.

$$\left(7000m^{2}-235m\right)c=2a$$

Divide both sides by 7000m^{2}-235m.

$$\frac{\left(7000m^{2}-235m\right)c}{7000m^{2}-235m}=\frac{2a}{7000m^{2}-235m}$$

Dividing by 7000m^{2}-235m undoes the multiplication by 7000m^{2}-235m.

$$c=\frac{2a}{7000m^{2}-235m}$$

Divide 2a by 7000m^{2}-235m.

$$c=\frac{2a}{5m\left(1400m-47\right)}$$