Solve (16-x)^2+6^2=8^2+x^2

$$( 16 - x ) ^ { 2 } + 6 ^ { 2 } = 8 ^ { 2 } + x ^ { 2 }$$

Solve for x

$$x = \frac{57}{8} = 7\frac{1}{8} = 7.125$$

Steps for Solving Linear Equation

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

$$256-32x+x^{2}+6^{2}=8^{2}+x^{2}$$

Calculate 6 to the power of 2 and get 36.

$$256-32x+x^{2}+36=8^{2}+x^{2}$$

Add 256 and 36 to get 292.

$$292-32x+x^{2}=8^{2}+x^{2}$$

Calculate 8 to the power of 2 and get 64.

$$292-32x+x^{2}=64+x^{2}$$

Subtract x^{2} from both sides.

$$292-32x+x^{2}-x^{2}=64$$

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

$$292-32x=64$$

Subtract 292 from both sides.

$$-32x=64-292$$

Subtract 292 from 64 to get -228.

$$-32x=-228$$

Divide both sides by -32.

$$x=\frac{-228}{-32}$$

Reduce the fraction \frac{-228}{-32} to lowest terms by extracting and canceling out -4.

$$x=\frac{57}{8}$$