MYTUTOR SUBJECT ANSWERS

459 views

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

Beth D. GCSE Maths tutor, A Level Maths tutor, GCSE Music tutor

2 years ago

Answered by Beth, a GCSE Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

507 SUBJECT SPECIALISTS

£20 /hr

Charles B.

Degree: Classics (Bachelors) - Durham University

Subjects offered:Maths, Latin+ 1 more

Maths
Latin
Classical Civilisation

“About me I'm a passionate classicist particularly focused on ancient military warfare  currently studying classics at Durham University. I've been studying Latin and  Ancient History since I was 9 years old, picking up Ancient Greek at ...”

£18 /hr

Mark H.

Degree: Mathematics MMath (Masters) - Manchester University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Hello there, I'm Mark and I study Mathematics at the University of Manchester! Let me help you achieve your best! ”

MyTutor guarantee

£18 /hr

Dominic K.

Degree: Chemical Engineering (Masters) - Leeds University

Subjects offered:Maths, Chemistry+ 1 more

Maths
Chemistry
Biology

“I am studying Chemical Engineering at Leeds University. I took 4 science A-Levels and have previous experience tutoring GCSE students whilst in 6th Form.”

About the author

Beth D.

Currently unavailable: for new students

Degree: Maths (Bachelors) - Exeter University

Subjects offered:Maths, Music

Maths
Music

“Hi, I’m Beth and I’m studying Maths at Exeter University. I achieved A*A*A in Maths, Further Maths and Music A-Levels and I am looking forward to teaching these subjects to be ready for the GCSE and A-Level exams! With 3 years of tuto...”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

How would you solve a quadratic equation by factorising?

How do i solve a system of 2 equations?

How to add fractions

Jill takes out a loan of £6000 to get a car. The loan has a compound interest of 3% and she takes it out for 4 years. a) How much interest has Jill accrued after 2 years? b) What is the total amount to be paid after 4 years?

View GCSE Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok