Solve the quadratic 2x^2+7x+6 by completing the square

All quadratic equations take the general form:


The first step used to comlete the square is to divide the whole equation by the a term, in our case 2:

1)        x2+(7/2)x+3=0

We then move our c term to the right hand side of the equation by subtracting from both sides:

2)        x2+(7/2)x=_3

Let us, for a moment, just examine the left hand side of this equation. We can see that:

3)        (x+7/4)2=x2+(7/2)x+(7/4)2


4)         x2+(7/2)x=(x+7/4)2-(7/4)2

Inserting equation 4 into equation 2 gives:

5)        (x+7/4)2-(7/4)2=_3

We can re-arrange to get:

6)        (x+7/4)2=_3+(7/4)2

Simplifying the right hand side gives:

7)        (x+7/4)2=1/16

Taking the square root of both sides gives(baring in mind that taking the square root of a number gives us a positive and a negative number):

8)        x+7/4=+1/4

Finally subtracting 7/4 leaves us with our answer:

9)        x=_3/2 or x=_2

Henry N. 11 Plus Maths tutor, GCSE Maths tutor, IB Maths tutor, A Lev...

1 year ago

Answered by Henry, a GCSE Maths tutor with MyTutor

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


£20 /hr

Emily L.

Degree: Law (Bachelors) - Durham University

Subjects offered:Maths, English Literature+ 1 more

English Literature

“I am a first year undergraduate reading Law at Durham University. Prior to this, I attended the Tiffin Girls' School in Kingston upon Thames where I studied English Literature, Chemistry and Fine Art at A2 Level (with additional Mathe...”

Marco-Iulian G. GCSE Maths tutor, Uni Admissions Test .MAT. tutor, A ...
£18 /hr

Marco-Iulian G.

Degree: Mathematics&Computer Science (Masters) - Bristol University

Subjects offered:Maths, Further Mathematics + 2 more

Further Mathematics

“I'm in my first year at University of Bristol, studying Mathematics and Computer Science MEng. From an early age I started to participate in lots of contests and maths olympiads, and the experience I achieved along the way enriched bo...”

£18 /hr

Georgia S.

Degree: Mathematics (Bachelors) - Bath University

Subjects offered:Maths, Design & Technology

Design & Technology

“Hi, I'm Georgia. I'm a Maths student with a passion for learning and with enough enthusiasm to inspire anyone to love Maths too!”

About the author

Henry N.

Currently unavailable: for regular students

Degree: Physics (Masters) - Bristol University

Subjects offered:Maths


“About me I am a second year physics student at the University of Bristol, with a keen interest inmaths and phsyics. Over the past few years my life has been completely filled with maths and I hope that my fascination for the subject ...”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

How do I solve a simple simultaneous equation?

Integrate ∫_(-1)^1 3/√(x+2) dx using the substitution u x+2

When do I use a cosine rule over a sine rule?

Factorise fully x^2+6x+5=0

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