Solve 36=(9-b)^2-b^2

$$36 = ( 9 - b ) ^ { 2 } - b ^ { 2 }$$

Solve for b

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

Steps for Solving Linear Equation

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

$$36=81-18b+b^{2}-b^{2}$$

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

$$36=81-18b$$

Swap sides so that all variable terms are on the left hand side.

$$81-18b=36$$

Subtract 81 from both sides.

$$-18b=36-81$$

Subtract 81 from 36 to get -45.

$$-18b=-45$$

Divide both sides by -18.

$$b=\frac{-45}{-18}$$

Reduce the fraction \frac{-45}{-18} to lowest terms by extracting and canceling out -9.

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