SOLUTION: Please help me find the real number solutions of this equation: {{{ 18x^3=50x }}} Thank you!

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Question 420033: Please help me find the real number solutions of this equation:
+18x%5E3=50x+

Thank you!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
18x%5E3=50x
In general, to solve equations where the variable has exponents larger than 1, you:
  • Get one side of the equation to be zero.
  • Factor the the other side.
  • Use the Zero Product Property.
  • Solve the equations from the Zero Product Property.

So we start by subtracting 50x from each side:
18x%5E3-50x+=+0
Now we factor. And factoring always starts with the Greatest Common Factor (GCF). The GCF is 2x:
2x%289x%5E2-25%29+=+0
The second factor is a difference of squares so it will factor according to the a%5E2-b%5E2+=+%28a%2Bb%29%28a-b%29 pattern:
2x(3x+5)(3x-5) = 0
We are finished factoring. The Zero Product Property tells us this (or any) product can be zero only if one (or more) of the factors is zero. So:
2x = 0 or 3x+5 = 0 or 3x-5 = 0
Solving each of these we get:
x = 0 or x = -5/3 or x = 5/3
These are the three real solutions to your equation.

P.S. "Exponential equations" are equations where the variable is in the exponent. Your equation is what is called a "Polynomial equation". Posting your problems under the right category may result in faster responses from the tutors.