Question 49698: Could you please help me with this problem? Every time I try, I end up with decimal coefficients or fractions, or both.
-4x=10x^2-24x^3
Answer by hulamc723(15)   (Show Source):
You can put this solution on YOUR website! -4x=10x^2-24x^3
First, add 4x to both sides so you get 10x^2-24x^3+4x=0
Then, put the monomials in descending order (-24x^3+10x^2+4x=0)
Now, factor out a 2x form the equation 2x(-12x^2+5x+2)=0
Now we are going to set up a table to solve for the problem
To do the table, we need to have two sections; The sum of five and the product of -12 and 2 (-24)
To do this we need to find numbers that, when multiplied together, equal -24 and if, when added together, equal five, we know that they are the two numbers that we are going to need to factor the equation!
Sum of 5 Product of -24
-23(not option) -24,1
23(not option) 24,-1
-10(not option) -12,2
10(not option) 2,-12
2(not option) 6,-4
-2(not option) -4,6
Now, since none of the numbers add up to 5, we are going to need to use the quadratic formula
x=-b +or- the square root of b^2-4(a)(c)/2a
now a=-12, b=5, and c=2
so, -5 +or- the square root of 5^2-4(-12)(2)/2(-12)
-5 +or- the square root of 25+96/-24
-5 +or- 11/24
-16/24 and 6/24 or (-2/3 and 1/4)
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