Solve left(x-8right)^2+15^2=x^2

$${ \left(x-8 \right) }^{ 2 } + { 15 }^{ 2 } = { x }^{ 2 }$$

Solve for x

$$x = \frac{289}{16} = 18\frac{1}{16} = 18.0625$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-8\right)^{2}.

$$x^{2}-16x+64+15^{2}=x^{2}$$

Calculate 15 to the power of 2 and get 225.

$$x^{2}-16x+64+225=x^{2}$$

Add 64 and 225 to get 289.

$$x^{2}-16x+289=x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-16x+289-x^{2}=0$$

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

$$-16x+289=0$$

Subtract 289 from both sides. Anything subtracted from zero gives its negation.

$$-16x=-289$$

Divide both sides by -16.

$$x=\frac{-289}{-16}$$

Fraction \frac{-289}{-16} can be simplified to \frac{289}{16} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{289}{16}$$