How do you complete the square?

Say you start with a general equation of x2+ax+b=0. (If the x2 has a coefficient the you will need to divide by that first.)

You need to move to the equation (x+a/2)2 -(a/2)2+b=0. Then put all of the constants together on the other side and square root everything so you end up with x-a/2 equalling plus or minus the square root of (a/2)2-b. You can then move to x equalling a/2 plus or minus the square root of (a/2)2-b.

For example, x2+6x+2=0 --> (x+3)2-32+2 =0 --> (x+3)2 =7 --> x+3 =+/-sqrt(7) --> x=-3+/-sqrt(7)

BC
Answered by Bryony C. Maths tutor

2699 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve 3(2x + 5) = 4 – x


Find the length of the longest side in this triangle.


Simplify fully (3x^2 -8x- 3)/(2x^2-6x)


Find the coordinates of the mid-point AB where A (-3,-3) and B (1,3)


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences