Solve 12^2+x^2=(8-x)^2

$$12 ^ { 2 } + x ^ { 2 } = ( 8 - x ) ^ { 2 }$$

Solve for x

$$x=-5$$

Steps for Solving Linear Equation

Calculate 12 to the power of 2 and get 144.

$$144+x^{2}=\left(8-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(8-x\right)^{2}.

$$144+x^{2}=64-16x+x^{2}$$

Add 16x to both sides.

$$144+x^{2}+16x=64+x^{2}$$

Subtract x^{2} from both sides.

$$144+x^{2}+16x-x^{2}=64$$

Combine x^{2} and -x^{2} to get 0.

$$144+16x=64$$

Subtract 144 from both sides.

$$16x=64-144$$

Subtract 144 from 64 to get -80.

$$16x=-80$$

Divide both sides by 16.

$$x=\frac{-80}{16}$$

Divide -80 by 16 to get -5.

$$x=-5$$