Quadratic Expressions

Completing the Square

Exercise 1

Complete the square on each of the following.

(a) x - 6x + 5

(b) 2z + 8z + 9

(c) 2w - 5w + 7

(d) 3y + 2y + 2

Solution

(a) Here x - 6x + 5 = [x - 6x] + 5

= [x - 6x + (3) - (3)] + 5

= [(x - 3) - 9] + 5

= (x - 3) - 4

(b) 2z + 8z + 9 = 2[z + 4z] + 9

= 2[z + 4z + (2) - (2)] + 9

= 2[(z + 2) - 4] + 9

= 2(z + 2) + 1

(c)

(d)

Quiz

Which of the expressions below is obtained after completing the square on 2x - 3x + 5?

Solution

We have 2x - 3x + 5 = x 3