Solve x^2+8^2=(16-x)^2

$$x ^ { 2 } + 8 ^ { 2 } = ( 16 - x ) ^ { 2 }$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Calculate 8 to the power of 2 and get 64.

$$x^{2}+64=\left(16-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(16-x\right)^{2}.

$$x^{2}+64=256-32x+x^{2}$$

Add 32x to both sides.

$$x^{2}+64+32x=256+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}+64+32x-x^{2}=256$$

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

$$64+32x=256$$

Subtract 64 from both sides.

$$32x=256-64$$

Subtract 64 from 256 to get 192.

$$32x=192$$

Divide both sides by 32.

$$x=\frac{192}{32}$$

Divide 192 by 32 to get 6.

$$x=6$$