Solve (4-x)^2=2^2+x^2

$$( 4 - x ) ^ { 2 } = 2 ^ { 2 } + x ^ { 2 }$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4-x\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

$$16-8x+x^{2}=4+x^{2}$$

Subtract x^{2} from both sides.

$$16-8x+x^{2}-x^{2}=4$$

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

$$16-8x=4$$

Subtract 16 from both sides.

$$-8x=4-16$$

Subtract 16 from 4 to get -12.

$$-8x=-12$$

Divide both sides by -8.

$$x=\frac{-12}{-8}$$

Reduce the fraction \frac{-12}{-8} to lowest terms by extracting and canceling out -4.

$$x=\frac{3}{2}$$