MYTUTOR SUBJECT ANSWERS

738 views

What are the different methods of solving quadratic equations?

For your maths GCSE it is important that you understand the three main methods of solving quadtratics: factorisation, completing the square, and using the quadratic formula.

1. Factorisation:

The first step for factorisation is to see if a common factor can be taken out, this is the easiest way of solving a quadratic.

For example:
2x+ 4x = 0
In the case a factor of 2x can be taken out, making the equation look like this:
2x(x+2) = 0 
This would then be solved by setting each part equal to zero,
2x = 0 and x+2=0.
Rearranging these equations gives us the final solutions of 
x = 0 and x = -2.

If a common factor cannot be found, the next step is to try and put the equation into two brackets that are multiplied together.

For example:
x2+5x+6=0
Would be rewritten as:
(x+2)(x+3)=0
^^^ when these brackets are multiplied out they give the original equation. 

So in order to split the equation into two brackets we have to know which numbers are needed. The solution will be of the form
(ax+b)(cx+d) = 0, where a,b,c and d are integers. 

So in our example,
a * c must equal 1 to give us the original 1x2.
a * d + b * c must be equal to 5 to give us 5x.
And b * d must be equal to 6 to give us our constant. 

2. Completing the square:

To 'complete the square' of a quadratic, the initial equation is rewritten as a (x + constant) bracket squared minus another constant to give the same value as the starting equation. This is easier shown than explained with words.

For example:

x2+10x+20 = 0
First, the coefficient of x (the ten infront of the x) is halved, and this is the constant used in the bracket with x.
This gives us:
(x+5)2  
But we want (x+5)2 + a constant to be equal to x2+10x+30 = 0.

If we expand the squared bracket we get the xand the 10x that we need, but we get a +25, when we need +20.

To fix this we just take off another 5 after our squared bracket giving us a final equation of 
(x+5)2  - 5 = 0  

To solve for x we just add 5 to both sides and take the square root. 
(x+5) = 5
x + 5 = +/- sqrt(5)
x = - 5 +/- sqrt(5)

3. Quadratic formula:

The last way of solving a quadratic is using the quadratic formula. 

In the following example a, b, and represent the integers in front of each part of the quadratic.

For example:

axbx + = 0 

To solve this using the quadratic formula, the integers just have to be subbed into the following equation:

x = [-b +/- sqrt (b2 - 4ac)] / 2a

This is quite difficult to type out but easy to actually use.

End:
I hope this step by step guide of the methods of solving quadratic equations has been useful!

Lois M. GCSE Maths tutor, A Level Maths tutor, GCSE Physics tutor

2 years ago

Answered by Lois, a GCSE Maths tutor with MyTutor


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

780 SUBJECT SPECIALISTS

£36 /hr

Dario P.

Degree: Computer Science (Doctorate) - Manchester University

Subjects offered:Maths, Italian+ 3 more

Maths
Italian
ICT
Computing
-Personal Statements-

“PhD Student in Computer Science with a passion for interdisciplinary research and teaching”

£18 /hr

Francesco D.

Degree: Medicine (Bachelors) - Oxford, Merton College University

Subjects offered:Maths, Human Biology+ 6 more

Maths
Human Biology
Chemistry
.BMAT (BioMedical Admissions)
-Personal Statements-
-Oxbridge Preparation-
-Medical School Preparation-

“I'm a second year medical student at Oxford University. Tutorials are fun, productive and tailored to you!”

£24 /hr

Steven A.

Degree: Bioscience (Masters) - Durham University

Subjects offered:Maths, Science+ 5 more

Maths
Science
Human Biology
English
Chemistry
-Personal Statements-

“Hi! I'm Steven and studying Biomedical Science at Durham. I'm friendly, approachable, and passionate for my subjects.”

About the author

Lois M.

Currently unavailable: for new students

Degree: Physics (Masters) - Exeter University

Subjects offered:Maths, Physics

Maths
Physics

“Hi! I'm Lois and I am currently in my second year of studying Physics at the University of Exeter. The past few years of my life have been filled to the brim with maths and physics, so I'm excited to be able to share what I've learned...”

You may also like...

Posts by Lois

What are the different methods of solving quadratic equations?

What are the different ways that energy can be transferred?

Other GCSE Maths questions

Expand and simplify (x+6)(x+4)

Can you solve the following 2 simultaneous equations; y=6x-2 and x^2-4x+19=y?

Expand and simplify the following; (2 + 3^0.5)^2 - (2 - 3^0.5)^2

What is the easiest way to expand quadratic equations?

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