How to complete the square?

This is a handy trick for quadratic equations ax^2 + bx + c = 0.

e.g. (x^2 + 5x + 6). So a = 1, b = 5 and c = 6.

To complete the square, let x^2 + 5x + 6 = 0. Then, take 6 to the other side to get x^2 + 5x = -6.

Now focus on x^2 + 5x. You need to divide 5 by 2 ( = 2.5) and write in the form (x + (b/2))^2 - (b/2)^2 = -6. So you get (x + 2.5)^2 - (2.5)^2 = -6. This equals to (x + 2.5)^2 = 0.25 as (2.5)^2 - 6 = 0.25. Then rearrange for x. (x + 2.5) = +- 0.5. So x = -3 and x = -2.

JP
Answered by Jigar P. Maths tutor

4675 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Whats the Product rule for differentiation and how does it work?


The function f(x) is defined by f(x) = 1 + 2 sin (3x), − π/ 6 ≤ x ≤ π/ 6 . You are given that this function has an inverse, f^ −1 (x). Find f^ −1 (x) and its domain


Given the two curves y1 and y2, verify the two curves intersect at (-5,0) and (2,0)


Solve the differential equation dy/dx=(y^(1/2))*sin(x/2) to find y in terms of x.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2026 by IXL Learning