I have an integration exam tomorrow and I need to understand how we get$$\Biggl( w+\frac{3}{2}\Biggl)^2$$

<http://tutorial.math.lamar.edu/Solutions/CalcII/IntegralsWithQuadratics/Prob1.aspx>

I was under the impression that it should be done:

$$w^2+3w+\frac{3}{2}^2+\frac{3}{2}$$

and $$w^2+3x+\frac{3}{2}^2$$should get factored and then get something like:$$(w+a)^2+\frac{3}{2}$$

Its been a long time since I have had to integrate with methods like this. Please clear up any confusion.