Solve (x-4)^2+6^2=x^2

$$( x - 4 ) ^ { 2 } + 6 ^ { 2 } = x ^ { 2 }$$

Solve for x

$$x = \frac{13}{2} = 6\frac{1}{2} = 6.5$$

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}.

$$x^{2}-8x+16+6^{2}=x^{2}$$

Calculate 6 to the power of 2 and get 36.

$$x^{2}-8x+16+36=x^{2}$$

Add 16 and 36 to get 52.

$$x^{2}-8x+52=x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-8x+52-x^{2}=0$$

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

$$-8x+52=0$$

Subtract 52 from both sides. Anything subtracted from zero gives its negation.

$$-8x=-52$$

Divide both sides by -8.

$$x=\frac{-52}{-8}$$

Reduce the fraction \frac{-52}{-8} to lowest terms by extracting and canceling out -4.

$$x=\frac{13}{2}$$