Solve (x-5)^2=(x-8)^2

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

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-5\right)^{2}.

$$x^{2}-10x+25=\left(x-8\right)^{2}$$

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

$$x^{2}-10x+25=x^{2}-16x+64$$

Subtract x^{2} from both sides.

$$x^{2}-10x+25-x^{2}=-16x+64$$

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

$$-10x+25=-16x+64$$

Add 16x to both sides.

$$-10x+25+16x=64$$

Combine -10x and 16x to get 6x.

$$6x+25=64$$

Subtract 25 from both sides.

$$6x=64-25$$

Subtract 25 from 64 to get 39.

$$6x=39$$

Divide both sides by 6.

$$x=\frac{39}{6}$$

Reduce the fraction \frac{39}{6} to lowest terms by extracting and canceling out 3.

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