Solve (x-2)^2=(x-9)^2

$$( x - 2 ) ^ { 2 } = ( x - 9 ) ^ { 2 }$$

Solve for x

$$x = \frac{11}{2} = 5\frac{1}{2} = 5.5$$

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}.

$$x^{2}-4x+4=\left(x-9\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-9\right)^{2}.

$$x^{2}-4x+4=x^{2}-18x+81$$

Subtract x^{2} from both sides.

$$x^{2}-4x+4-x^{2}=-18x+81$$

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

$$-4x+4=-18x+81$$

Add 18x to both sides.

$$-4x+4+18x=81$$

Combine -4x and 18x to get 14x.

$$14x+4=81$$

Subtract 4 from both sides.

$$14x=81-4$$

Subtract 4 from 81 to get 77.

$$14x=77$$

Divide both sides by 14.

$$x=\frac{77}{14}$$

Reduce the fraction \frac{77}{14} to lowest terms by extracting and canceling out 7.

$$x=\frac{11}{2}$$