Solve (8-x)^2-5^2=(4-x)^2+3^2

$$( 8 - x ) ^ { 2 } - 5 ^ { 2 } = ( 4 - x ) ^ { 2 } + 3 ^ { 2 }$$

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}.

$$64-16x+x^{2}-5^{2}=\left(4-x\right)^{2}+3^{2}$$

Calculate 5 to the power of 2 and get 25.

$$64-16x+x^{2}-25=\left(4-x\right)^{2}+3^{2}$$

Subtract 25 from 64 to get 39.

$$39-16x+x^{2}=\left(4-x\right)^{2}+3^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4-x\right)^{2}.

$$39-16x+x^{2}=16-8x+x^{2}+3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$39-16x+x^{2}=16-8x+x^{2}+9$$

Add 16 and 9 to get 25.

$$39-16x+x^{2}=25-8x+x^{2}$$

Add 8x to both sides.

$$39-16x+x^{2}+8x=25+x^{2}$$

Combine -16x and 8x to get -8x.

$$39-8x+x^{2}=25+x^{2}$$

Subtract x^{2} from both sides.

$$39-8x+x^{2}-x^{2}=25$$

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

$$39-8x=25$$

Subtract 39 from both sides.

$$-8x=25-39$$

Subtract 39 from 25 to get -14.

$$-8x=-14$$

Divide both sides by -8.

$$x=\frac{-14}{-8}$$

Reduce the fraction \frac{-14}{-8} to lowest terms by extracting and canceling out -2.

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