Hello there. To solve this quadratic equation using the method of completing squares, we need to remember some properties on binomial expansions.
First, remember that (a + b)² = a² + 2ab + b².
With this in mind, we want to find a value b that we can sum into x² + 3x and reach something like the expression in the line above.
So, we divide the second term coefficient by two
3/2
Now, square this term
9/4
Sum this term on both sides of the equation
x² + 3x + 9/4 = 40 + 9/4
Sum the fractions on the right hand side
x² + 3x + 9/4 = 169/4
Now, we can make the LHS return to its power form:
(x + 3/2)² =