#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
