Factor the expression 0 =9x^2 - 113x + 350

My mathlab says the answer is 0=(9x -50)(x-7)

Now I know the two number need to multiple to equal 350 and they are supposed to add to be -113... why do they not want them adding to equal -113.

I dont see the connection.

This only works when you have x² - Sx + P = 0.
0 =9x^2 - 113x + 350

So
x² - 113/9x + 350/9 = 0

F O I L = First, Outer, inner, last

F = 9x * x = 9x^2
O = 9x * -7 = -63x
I = -50 * x = -50x
L = -50 * -7 = 350

F + O + I + L = 9x^2 - 113x + 350

They aren't straight adding to -113 because you when you do the "Outer" step you are multiplying that -7 by 9, which you are neglecting to do which is why you're getting -57 when you add them. Straight adding them will only work if it is X^2 and not aX^2

This post was edited by RzChaos on Sep 30 2015 03:24pm

9x^2 - 113x + 350 = 0

This kind of expression is a common a.(x-x1).(x-x2) = 0, which is the same as ax^2 + bx + c = 0

All you have to do is find the roots (x1 and x2) of the equation using Baskara's formula:

x = (-b +/- √b^2 - 4.a.c) / 2.a

x = (113 +/- √12769 - 4.9.350) / 2.9

x = (113 +/- 13) / 18

So, x1 = (113 + 13) / 18 = 7
x2 = (113 - 13) / 18 = 50/9


Now getting the first expression:
a.(x-x1).(x-x2) = 0
9.(x-7).(x-50/9) = 0

We could finish here, but it is more simple if you multiply the 9 for the term (x-50/9)
So, we will have 9x - 9.50/9 = 9x - 50

The final answer is (x-7).(9x-50)

I hope I could help.