How do I complete the square of an equation?

First off, write your equation in the form:

ax^2+by+c=0

with a, b and c being your constant coefficients. 

First, we will factorise out a such that:

a(x^+(b/a)x)+c

Now divide b by 2. Then write 

a(x+(b/2a))^2

If you multiply this out you should get a(x^+(b/a)x+d)

Then times everything by a again to give ax^2+bx+ad

The final stage is to add a constant on the end which will get you from ad to c in the final expansion.

To do this we want ad+m=c where m is the constant we are trying to find. Therefore m=c-ad.

Our final answer will be:

ax^+bx+c=a(x+(b/2a))^+m .

 

This is much easier to see with an example:

Complete the square of 4x^2+4x=-6

We need to rearrange this to 4x^2+4x+6=0.

First we factorise out the 4:

4(x^2+x)+6=0 

Now we follow through the rest of the steps:

4(x+1/2)^2=4(x^2+x+1/4)=4x^2+4x+1

1+m=6

m=5

So the final answer is

4x^2+4x+6=4(x+1/2)^2+5=0

BD
Answered by Beth D. Maths tutor

4440 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

15 machines work at the same rate, 15 machines can complete an order in 8 hours, however 3 of the machines break down after 6 hours. The other machines continue until the order is complete. In total how many hours does EACH machine work? (3 mark question)


How do I solve simultaneous equations when one of the equations is not linear?


x^2 - 10x + 33 ≡ (x - a)^2 + b. Work out the value of a and b.


Solve the following simultaneous equation for x and y: 2x + 5y = 8, 4x + y = 7


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