Question

Complete the square for x^2 + 3x + 1

Answer 1

(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