SOLUTION: What are the factors for the product of -36 and the sum of 12? The original problem was 2q/2q+3 -2q/2q-3=1

Algebra.Com
Question 809383: What are the factors for the product of -36 and the sum of 12?
The original problem was
2q/2q+3 -2q/2q-3=1
Found 2 solutions by edjones, KMST:
Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
2q/2q+3 - 2q/2q-3 = 1
4q^2-6q-4q^2-6q=4q^2-9
4q^2+12q-9=0
q=-3(sqrt2+1)/2, q=3(sqrt2-1)/2 see below
.
Ed
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=288 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.621320343559642, -3.62132034355964. Here's your graph:
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
Not all quadratic equations can be solved by factoring.
Factoring works when the solutions are rational numbers.
That is not the case for .
I would solve that by completing the square,
or by applying the quadratic formula.

Completing the square:
-->
Looking at , you realize that it is part of
,
so you add 9 to both sides of to get
-->
Either
-->-->-->
or
-->-->-->
Both solutions can bew expressed with the formula


Applying the quadratic formula works well too, but it is kind of boring.
(I only use it when the square to be completed is not too obvious).
Assuming that you remember the formula and apply it flawlessly, you end up with
RELATED QUESTIONS

what are the factors of q3-q2+2q-2 (answered by jim_thompson5910)
Simplify by removing factors of 1. 2q^2+2q/14q^2+4q. the simplified form is:... (answered by Tatiana_Stebko)
please help what are the factors of... (answered by Nate)
What are the factors of... (answered by jim_thompson5910)
what is the value of 2q - 3... (answered by MathLover1)
the problem is 14-(2q+5)=... (answered by stanbon)
2q+3 (answered by ikleyn)
What is... (answered by ReadingBoosters)
how do you simplify the expression 3/8p^2q +... (answered by Nate)