Solve x^2=left(x-10right)^2+24^2

$${ x }^{ 2 } = { \left(x-10 \right) }^{ 2 } + { 24 }^{ 2 }$$

Solve for x

$$x = \frac{169}{5} = 33\frac{4}{5} = 33.8$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-10\right)^{2}.

$$x^{2}=x^{2}-20x+100+24^{2}$$

Calculate 24 to the power of 2 and get 576.

$$x^{2}=x^{2}-20x+100+576$$

Add 100 and 576 to get 676.

$$x^{2}=x^{2}-20x+676$$

Subtract x^{2} from both sides.

$$x^{2}-x^{2}=-20x+676$$

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

$$0=-20x+676$$

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

$$-20x+676=0$$

Subtract 676 from both sides. Anything subtracted from zero gives its negation.

$$-20x=-676$$

Divide both sides by -20.

$$x=\frac{-676}{-20}$$

Reduce the fraction \frac{-676}{-20} to lowest terms by extracting and canceling out -4.

$$x=\frac{169}{5}$$