Solve x^2 + x -12= 0 for all values of x.

This is a quadratic equation so there are two main methods you can use to solve it- factorising and completing the square.

My preferred method and the one I will demonstrate is factorisation.

The above equation will take the form:

(x + a)(x +b) = 0

Therefore if we multiply out the brackets we get:

x^2 + (a+b)x +ab = 0

This means that

(a+b) = 1 (the coefficient of x)


ab = 12

From trial and error we find the values for a and b which are 

a= -3

b= 4

So x^2 + x -12= 0 can be written as (x-3)(x+4)= 0

When we multiply by 0 we get 0 therefore

x-3 = 0 or 

x+4= 0

From rearranging the above equations we find the answer is x = 3 or x = -4

Sam F. GCSE Maths tutor

5 months ago

Answered by Sam, a GCSE Maths tutor with MyTutor

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


£36 /hr

Andres O.

Degree: PhD in Theoretical Particle Physics (Doctorate) - Durham University

Subjects offered:Maths, Physics+ 2 more

-Oxbridge Preparation-

“I am a patient and experienced tutor with a lot of enthusiasm for Mathematics and Physics. ”

£22 /hr

Prina S.

Degree: Environmental Geoscience (Masters) - Bristol University

Subjects offered:Maths, Physics+ 2 more


“Hello there! My name is Prina and I'm a first year Environmental Geoscience at the University of Bristol. My love for science was instilled in me by those who taught me and I hope to share my passion in the same way through exciting an...”

£18 /hr

Philip C.

Degree: Mechanical Engineering (Masters) - Imperial College London University

Subjects offered:Maths


“About me: I am a 4th year Mechanical Engineering student at Imperial College London. I have studied Mathematics across all levels and use it on a daily basis during my degree. I am extremely passionate about helping others gain a deep...”

About the author

Sam F.

Currently unavailable: until 05/01/2018

Degree: Economics and Philosophy (Bachelors) - York University

Subjects offered:Maths


“About me: I am an Economics and Philosophy student at the University of York. I have always found Maths and all problems Maths related to be fun and rewarding and hope that you, through my sessions, will too! I am very patient and fr...”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

Find the volume and surface area of a cylinder, of length 20cm and radius 5cm.

Factorise x^2+7x+10 to find the roots of the equatino x^2+7x+10=0

How do I factorise quadratic equations?

The area of a square is 49cm^2. The perimeter of the square is equal to the circumference of a circle. what is the radius of the circle?

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