1) Multiply the coefficient of x by the constant.
5xx7=35
2) Find a pair of numbers that add to make the second term and multiply to make the third. We can easily spot here that only 35 and 1 can make 34
3) Work out which is negative and which is positive if necessary, as the second term is -34x, the numbers must be -35x and +x
Keep the quadratic constant at it's original, we just need to multiply to find the pair of numbers
5x^2-34x-7 -> 5x^2+x-35x-7
4) Factor out the first 2 terms:
5x^2+x -> x(5x+1)
5) Factor out the second 2 terms.
-35x-7 -> -7(5x+1)
Notice that both brackets are the same
So the first bracket is (5x+1)
6) The second bracket is the other 2 terms.
We have:
x(5x+1)-7(5x+1)
therefore The other bracket must be (x-7)
7) Solve:
(5x+1)(x-7)=0
8) Solve each bracket separately:
5x+1=0
-> 5x=-1
-> x=-1/5
x-7=0
-> x=7
Therefore these are our two answers.
x=7 and x=-1/5
Remember you can always expand the brackets to check the answer
