Solve (x-2)^2=(x-3)^2

$$( x - 2 ) ^ { 2 } = ( x - 3 ) ^ { 2 }$$

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

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

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$x^{2}-4x+4=x^{2}-6x+9$$

Subtract x^{2} from both sides.

$$x^{2}-4x+4-x^{2}=-6x+9$$

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

$$-4x+4=-6x+9$$

Add 6x to both sides.

$$-4x+4+6x=9$$

Combine -4x and 6x to get 2x.

$$2x+4=9$$

Subtract 4 from both sides.

$$2x=9-4$$

Subtract 4 from 9 to get 5.

$$2x=5$$

Divide both sides by 2.

$$x=\frac{5}{2}$$