Solve x^2-5*x+6=0

  • Google+ icon
  • LinkedIn icon
  • 874 views

There are 2 methods we can use here.

Method 1 - Factorisation

If we can rewrite the equation so that it looks like (x+a)*(x+b)=0, where 'a' and 'b' are numbers, then we can easily find a solution. If one or both of the terms inside the brackets equals 0, then their product is also 0. This means the solution(s) are the values of x such that x+a=0 or x+b=0.

Multiplying out the brackets of (x+a)*(x+b)=0 gives x2+(a+b)*x+a*b=0. If we match up the terms with the equation we want to solve (called comparing coefficients), we see that we want two numbers 'a' and 'b' so that a+b=-5, and a*b=6. The two numbers which satisfy this are -2 and -3, so these are our values for 'a' and 'b'.

Now we can write our equation as (x-2)(x-3)=0 (you can check yourself this can be multiplied out to give the original equation!)

If x-3=0 then x=3, and if x-2=0 then x=2, so these are our two solutions.

Method 2 - Quadratic Formula

This method can be used when you can't easily 'see' the numbers to use to factorise the equation.

The quadratic formula states that for an equation of the form a*x2+b*x+c=0, where 'a', 'b', and 'c' are numbers, then

x=(-b+-sqrt(b2-4*a*c)/(2*a)

For our equation a=1, b=-5 and c=6, which can then be substituted into the formula. Again you can check yourself that it simplifies to give the same answers as method 1

Hannah D. A Level Maths tutor, GCSE Maths tutor, A Level Further Math...

About the author

is an online GCSE Maths tutor with MyTutor studying at Bristol University

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

95% of our customers rate us

Browse 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