You can put this solution on YOUR website!
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:
Now we factor. And factoring always starts with the Greatest Common Factor (GCF). The GCF is 2x:
The second factor is a difference of squares so it will factor according to the
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.