SOLUTION: I would like help with factoring trinomials so I can solve an equation. "The area of a triangle is 75 square inches. One side of the triangle is 35 inches less than 3 times the

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I would like help with factoring trinomials so I can solve an equation. "The area of a triangle is 75 square inches. One side of the triangle is 35 inches less than 3 times the       Log On


   

Question 739864: I would like help with factoring trinomials so I can solve an equation.
"The area of a triangle is 75 square inches. One side of the triangle is 35 inches less than 3 times the length of the altidude to that side. Fidn the length of that side."
here's what I have so far:
1/2a(3a-35)=75
(multiply 1/2 by 2, and 75 by 2 to get rid of fraction)
a(3a-35)=150
I need to make 150=0
3a^2-35a-150=0
This is where i'm stuck.
I cannot factor this down to get the format:
(x+x)(x-x) which is needed to solve my equation x+x=0, x-x=0
maybe i wrote my equation wrong from the word problems?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The altitude's value is the height of the triangle. You correctly expressed the "one side" for the triangle, which is treated as the base, since the altitude has an endpoint on this side.

%281%2F2%29%283a-35%29%2Aa=75
or
%281%2F2%29a%283a-35%29=75

a%283a-35%29=150
3a%5E2-35a=150
highlight%283a%5E2-35a-150=0%29, so you have done well so far. You really want to FACTOR that trinomial? Try if you want, but solution to quadratic formula might be more comfortable.

Using the positive square root of discriminant,
a=%2835%2Bsqrt%2835%5E2-4%2A3%2A%28-150%29%29%29%2F%282%2A3%29
a=%2835%2Bsqrt%2835%5E2%2B1800%29%29%2F%282%2A3%29
a=%2835%2Bsqrt%283025%29%29%2F%282%2A3%29
a=%2835%2B55%29%2F%282%2A3%29
a=90%2F6
highlight%28a=15%29

FACTOR?
You could again, as I said, try to factor. You may first try including binomial, (a-15) because one of your pairs of numbers to get 150 as a product is 15 and 10. You would want other constant be positive number. Best guess (educated guess) is (3a+10) and (a-15).
CHECKING THAT: %283a%2B10%29%28a-15%29=3a%5E2-45a%2B10a-150, looks like good.