Solve (x-7)^2=(5-x)^2

$$( x - 7 ) ^ { 2 } = ( 5 - x ) ^ { 2 }$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-7\right)^{2}.

$$x^{2}-14x+49=\left(5-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5-x\right)^{2}.

$$x^{2}-14x+49=25-10x+x^{2}$$

Add 10x to both sides.

$$x^{2}-14x+49+10x=25+x^{2}$$

Combine -14x and 10x to get -4x.

$$x^{2}-4x+49=25+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-4x+49-x^{2}=25$$

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

$$-4x+49=25$$

Subtract 49 from both sides.

$$-4x=25-49$$

Subtract 49 from 25 to get -24.

$$-4x=-24$$

Divide both sides by -4.

$$x=\frac{-24}{-4}$$

Divide -24 by -4 to get 6.

$$x=6$$