SOLUTION: I need help with this problem. 3x-75x^3=0. I should come up with 3 answers.

Question 112241: I need help with this problem. 3x-75x^3=0. I should come up with 3 answers.
Found 4 solutions by jim_thompson5910, checkley71, rapaljer, BrittanyM:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation

Factor out the GCF

Now factor using the difference of squares

Now set each factor equal to zero:
, , or

, , or Now solve for x in each case

So our solutions are

, , or
Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!
3X-75X^3=0
-3X(25X^2-1)=0
-3X(5X+1)(5X-1)=0
-3X=0
X=0/-3
X=0 ANSWER.
5X+1=0
5X=-1
X=-1/5 ANSWER.
5X-1=0
5X=1
X=1/5 ANSWER.

Answer by rapaljer(4671)   (Show Source): You can put this solution on YOUR website!

First, factor the common factor, which is 3x.

This factors again as the difference of two squares:

There are three solutions:
3x=0
x=0

1-5x=0
1=5x
x=1/5

1+5x=0
5x=-1
x=-1/5

R^2 Retired from SCC
Answer by BrittanyM(80)   (Show Source): You can put this solution on YOUR website!
We have to factor this equation before we can solve for its values of x.

Since both terms in the problem have 3x as a common factor, we can factor it out on the side:

3x -75x^3 = 0
3x(-25x + 1)

Now, we can use the bottoms up rule in order to get the equation into a reasonable form.

3x(x^2 - 25) = 0

This can be further factored to:
3x(x + 5)(x - 5) = 0

Let's remember to finish the bottoms up:
3x(5x + 1)(5x - 1) = 0

Nwe, we kow our first value of x is 0 because:
3x = 0
x = 0

And our second value comes from the next term:
(5x + 1) = 0
5x = -1
x = -1/5

And our third term comes from the final term:
(5x -1) = 0
5x = 1
x = 1/5
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