SOLUTION: I just solved a problem on my algebra test, and I am not sure how I did it... In regards to a rectangle with sides X and 2x+5, and area being 168 X(2x+5)=168 Solve for X W

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I just solved a problem on my algebra test, and I am not sure how I did it... In regards to a rectangle with sides X and 2x+5, and area being 168 X(2x+5)=168 Solve for X W      Log On


   

Question 366606: I just solved a problem on my algebra test, and I am not sure how I did it... In regards to a rectangle with sides X and 2x+5, and area being 168
X(2x+5)=168
Solve for X
While trying to work on it, I was factoring 168, and realized the factors 8,21 fit for X and 2x+5... it was an intuitive leap. I would like to know how to actually solve this properly
Found 2 solutions by Fombitz, ewatrrr:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%282x%2B5%29=168+
2x%5E2%2B5x=168
2x%5E2%2B5x-168=0
%282x%2B21%29%28x-8%29=0
Two solutions but only 1 is positive.
x-8=0
highlight%28x=8%29

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi, 

x(2x+5)=168 

2x^2 + 5x - 168 = 0

Yes, factoring works: 

Coming up with the product of -8*21 = 168 and using that

(2x +21)(x -8) = 0  

(2x + 21)=0

x = -(21/10) = -10.5

(x -8) = 0 

x = 8 

The quadratic equations "always" works as well:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-5+%2B-+sqrt%28+1369+%29%29%2F%284%29+

x+=+%28-5+%2B-+37%29%2F%284%29+

x = (-5 + 37)/4 = 8

x = (-5 -37)/4 = -42/4 = -21/2 = -10.5