How can I factorise a quadratic equation?

A quadratic equation is an equation of the form y = ax2 + bx + c where a, b and c are constants (for example 5, -2 or 0). To "solve" a quadratic equation we are finding the values of x that satisfy this equation For example the equation 9 = xhas 2 solutions, x = 3 and x = -3 (as when you replace x with these values, the equation is true, as 9 = 9). A quadratic equation can either have 0, 1 or 2 solutions.

There are many ways of finding what values satisfy these equations, here is one that always works.

The quadratic formula: First rearrange your equation so that it is in the form 0 = ax2 + bx + now take the general quadratic formula which is given by x = (-b +- sqrt(b- 4ac)) / 2a +- in this case means one solution is given by adding, and one by subtracting (so you have to do it twice). Simply substituting our coefficients into this formula will give us our solutions.

For example let's take the equation 7 = x2 - 2x + 8

1) Rearrange to the appropriate format by moving the 7 onto the other side to give: x-2x + 1 = 0

2) Work out our coefficients, a = 1 b = -2 c = 1

3) Substitute these into our equation to give:

x = -((-2) +- sqrt ( (-2)^2 - 411)) / 2

 This simplifies to give

x = (2 +- sqrt (4 - 4)) / 2

which simplfies again to 1 +- 0, this means we have only one solution (as 1 + 0 and 1 - 0 both = 1), so our solution to this is x = 1.

Answered by Tom R. Maths tutor

2587 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How to Solve: (11 − w)/4 = 1 + w


Jorgen has 20 sweets in his pocket. The sweets are either blue or yellow. He picks a sweet and eats it and takes another sweet and eats it again. The probability of him picking two blue sweets is 6/30. How many yellow sweets does he have in his pocket.


Prove algebraically that the straight line with equation x - 2y = 10 is a tangent to the circle with equation x^2 + y^2= 20


Work out 51% of 400?


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