Solve x^2=130^2+(x-40)^2

$$x ^ { 2 } = 130 ^ { 2 } + ( x - 40 ) ^ { 2 }$$

Solve for x

$$x = \frac{925}{4} = 231\frac{1}{4} = 231.25$$

Steps for Solving Linear Equation

Calculate 130 to the power of 2 and get 16900.

$$x^{2}=16900+\left(x-40\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-40\right)^{2}.

$$x^{2}=16900+x^{2}-80x+1600$$

Add 16900 and 1600 to get 18500.

$$x^{2}=18500+x^{2}-80x$$

Subtract x^{2} from both sides.

$$x^{2}-x^{2}=18500-80x$$

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

$$0=18500-80x$$

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

$$18500-80x=0$$

Subtract 18500 from both sides. Anything subtracted from zero gives its negation.

$$-80x=-18500$$

Divide both sides by -80.

$$x=\frac{-18500}{-80}$$

Reduce the fraction \frac{-18500}{-80} to lowest terms by extracting and canceling out -20.

$$x=\frac{925}{4}$$