Solve (AD-10)^2=(15-AD)^2-25

$$( A D - 10 ) ^ { 2 } = ( 15 - A D ) ^ { 2 } - 25$$

Solve for A

$$A=\frac{10}{D}$$

$$D\neq 0$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(AD-10\right)^{2}.

$$A^{2}D^{2}-20AD+100=\left(15-AD\right)^{2}-25$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(15-AD\right)^{2}.

$$A^{2}D^{2}-20AD+100=225-30AD+A^{2}D^{2}-25$$

Subtract 25 from 225 to get 200.

$$A^{2}D^{2}-20AD+100=200-30AD+A^{2}D^{2}$$

Add 30AD to both sides.

$$A^{2}D^{2}-20AD+100+30AD=200+A^{2}D^{2}$$

Combine -20AD and 30AD to get 10AD.

$$A^{2}D^{2}+10AD+100=200+A^{2}D^{2}$$

Subtract A^{2}D^{2} from both sides.

$$A^{2}D^{2}+10AD+100-A^{2}D^{2}=200$$

Combine A^{2}D^{2} and -A^{2}D^{2} to get 0.

$$10AD+100=200$$

Subtract 100 from both sides.

$$10AD=200-100$$

Subtract 100 from 200 to get 100.

$$10AD=100$$

The equation is in standard form.

$$10DA=100$$

Divide both sides by 10D.

$$\frac{10DA}{10D}=\frac{100}{10D}$$

Dividing by 10D undoes the multiplication by 10D.

$$A=\frac{100}{10D}$$

Divide 100 by 10D.

$$A=\frac{10}{D}$$

Solve for D

$$D=\frac{10}{A}$$

$$A\neq 0$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(AD-10\right)^{2}.

$$A^{2}D^{2}-20AD+100=\left(15-AD\right)^{2}-25$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(15-AD\right)^{2}.

$$A^{2}D^{2}-20AD+100=225-30AD+A^{2}D^{2}-25$$

Subtract 25 from 225 to get 200.

$$A^{2}D^{2}-20AD+100=200-30AD+A^{2}D^{2}$$

Add 30AD to both sides.

$$A^{2}D^{2}-20AD+100+30AD=200+A^{2}D^{2}$$

Combine -20AD and 30AD to get 10AD.

$$A^{2}D^{2}+10AD+100=200+A^{2}D^{2}$$

Subtract A^{2}D^{2} from both sides.

$$A^{2}D^{2}+10AD+100-A^{2}D^{2}=200$$

Combine A^{2}D^{2} and -A^{2}D^{2} to get 0.

$$10AD+100=200$$

Subtract 100 from both sides.

$$10AD=200-100$$

Subtract 100 from 200 to get 100.

$$10AD=100$$

Divide both sides by 10A.

$$\frac{10AD}{10A}=\frac{100}{10A}$$

Dividing by 10A undoes the multiplication by 10A.

$$D=\frac{100}{10A}$$

Divide 100 by 10A.

$$D=\frac{10}{A}$$