Answer:
(x+3/2)^2 - 5/4
Explanation:
x^2 + bx + (b/2))^2 = (x+b/2))^2
use the formula (b/2)^2 in order to create a new term to complete the square
x^2 + 3x + 1
x^2 + 3x = - 1
basically divide the number next to the x and then square it
(b/2)^2 : b = 3 -> 3/2 -> (3/2)^2 = 9/4
basically divide the number next to the x by 2 and then square it
put 9/4 on both sides of the equal sign
x^2 + 3x + 9/4 = -1 + 9/4
x^2 + 3x + 9/4 = -4/4 + 9/4
(x + 3/2)^2 = 5/4
put 5/4 back to the left of the equal sign
(x + 3/2)^2 - 5/4