Solve AB^2+20^2=24^2

$$A B ^ { 2 } + 20 ^ { 2 } = 24 ^ { 2 }$$

Solve for A

$$A=\frac{176}{B^{2}}$$

$$B\neq 0$$

Steps for Solving Linear Equation

Calculate 20 to the power of 2 and get 400.

$$AB^{2}+400=24^{2}$$

Calculate 24 to the power of 2 and get 576.

$$AB^{2}+400=576$$

Subtract 400 from both sides.

$$AB^{2}=576-400$$

Subtract 400 from 576 to get 176.

$$AB^{2}=176$$

The equation is in standard form.

$$B^{2}A=176$$

Divide both sides by B^{2}.

$$\frac{B^{2}A}{B^{2}}=\frac{176}{B^{2}}$$

Dividing by B^{2} undoes the multiplication by B^{2}.

$$A=\frac{176}{B^{2}}$$

Solve for B (complex solution)

$$B=-4\sqrt{11}A^{-\frac{1}{2}}$$

$$B=4\sqrt{11}A^{-\frac{1}{2}}\text{, }A\neq 0$$

Solve for B

$$B=4\sqrt{\frac{11}{A}}$$

$$B=-4\sqrt{\frac{11}{A}}\text{, }A>0$$