Solve (8-x)^2=x^2+6^2

$$( 8 - x ) ^ { 2 } = x ^ { 2 } + 6 ^ { 2 }$$

Solve for x

$$x = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

Steps for Solving Linear Equation

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

$$64-16x+x^{2}=x^{2}+6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$64-16x+x^{2}=x^{2}+36$$

Subtract x^{2} from both sides.

$$64-16x+x^{2}-x^{2}=36$$

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

$$64-16x=36$$

Subtract 64 from both sides.

$$-16x=36-64$$

Subtract 64 from 36 to get -28.

$$-16x=-28$$

Divide both sides by -16.

$$x=\frac{-28}{-16}$$

Reduce the fraction \frac{-28}{-16} to lowest terms by extracting and canceling out -4.

$$x=\frac{7}{4}$$