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

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

Solve for x

$$x = \frac{9}{4} = 2\frac{1}{4} = 2.25$$

Steps for Solving Linear Equation

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

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

Add 2 and 16 to get 18.

$$x^{2}=18+x^{2}-8x$$

Subtract x^{2} from both sides.

$$x^{2}-x^{2}=18-8x$$

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

$$0=18-8x$$

Swap sides so that all variable terms are on the left hand side.

$$18-8x=0$$

Subtract 18 from both sides. Anything subtracted from zero gives its negation.

$$-8x=-18$$

Divide both sides by -8.

$$x=\frac{-18}{-8}$$

Reduce the fraction \frac{-18}{-8} to lowest terms by extracting and canceling out -2.

$$x=\frac{9}{4}$$