15w2 - 7w - 2 = 0

Question

Solve by factoring

Answer 1

Hi factoring this in easy way:

you have to multiply 15x2=30

then you have to find two numbers such as a1 x a2 = 30 and also the same numbers a1 +/- a2 = 7

just by thinking a little bit you can say that 10 and 3 are your number right?

10 x 3 = 30 and 10-3=7 (don't worry about signs yet)

les put the equation like this:

15w^2 -10W+3W -2 = 0      (I just changed -7W in function of the numbers a1 and a2 so -7W = -10W + 3W right?)

 

now lets order this in a better way

15W^2 + 3W -10W -2 = 0    ( I just re-ordered)

from the two first terms and the second two

3W(5W+1) - 2 (5W +1) = 0   (just took common factor between them)

now take common factor again ( 5W+1 is common between the two terms)

so

(5W+1) (3W-2) = 0

 

therefore w = -1/5 and w=2/3

 

hope this helped

Answer 2

One way is using the quadratic equation formula..you can google it. 

 

Or

 

what at are the factors of 15 and 2

15=5*3 or 15*1

2= 2*1

 

create a box.     

 

                      5w    3w

               2    10w   6w

               1     5w     3w

 

note that the 10w-3w will give 7w, since the 7w is negative then the bigger number between 10 and 3 must be negative. And since 2 is negative and 5 times 2 is 10, that will be the negative (-2*+1=-2)

 

(5w+1)(3w-2)

w=-1/5, w=2/3...it's written as the reciprocal.