Solve 100^2=(100-4a)^2+2a320

$$100 ^ { 2 } = ( 100 - 4 a ) ^ { 2 } + 2 a 320$$

Solve for a_320

$$a_{320}=8a\left(50-a\right)$$

Steps for Solving Linear Equation

Calculate 100 to the power of 2 and get 10000.

$$10000=\left(100-4a\right)^{2}+2a_{320}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(100-4a\right)^{2}.

$$10000=10000-800a+16a^{2}+2a_{320}$$

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

$$10000-800a+16a^{2}+2a_{320}=10000$$

Subtract 10000 from both sides.

$$-800a+16a^{2}+2a_{320}=10000-10000$$

Subtract 10000 from 10000 to get 0.

$$-800a+16a^{2}+2a_{320}=0$$

Add 800a to both sides. Anything plus zero gives itself.

$$16a^{2}+2a_{320}=800a$$

Subtract 16a^{2} from both sides.

$$2a_{320}=800a-16a^{2}$$

Divide both sides by 2.

$$\frac{2a_{320}}{2}=\frac{16a\left(50-a\right)}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$a_{320}=\frac{16a\left(50-a\right)}{2}$$

Divide 16a\left(50-a\right) by 2.

$$a_{320}=8a\left(50-a\right)$$

Solve for a (complex solution)

$$a=\frac{\sqrt{10000-2a_{320}}}{4}+25$$

$$a=-\frac{\sqrt{10000-2a_{320}}}{4}+25$$

Solve for a

$$a=\frac{\sqrt{10000-2a_{320}}}{4}+25$$

$$a=-\frac{\sqrt{10000-2a_{320}}}{4}+25\text{, }a_{320}\leq 5000$$