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)

Answered by Bryony C. Maths tutor

2333 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

The rectangles A and B have perimeters of 94cm and 56cm as shown below (insert diagram). Rectangle A: base = 2x cm, height = 3y cm. Rectangle B: base = (x+6)cm, height = (y+4)cm. Use an algebraic method to calculate the area of each rectangle. (8 marks)


Solve the simultaneous equation: 2x + 3y = 6, 3x + 2y = 5.


Solve the simultaneous equations: 3x + y = -9, x^2 + 2x - 3 = y


There are 35 people in a group. x(x+1) of them have a blue car, 5x of them have a red car, 4 have a blue and a red car and 4x-8 do not have car. Work out the probability that a person who has a blue car, has a red car as well.


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 2013–2024

Terms & Conditions|Privacy Policy
Cookie Preferences