Simplifying the Expression: 5^2x - 6.5^x + 1 + 125 = 0
In this article, we will explore how to simplify the expression 5^2x - 6.5^x + 1 + 125 = 0. This expression involves exponential functions and polynomials, and we will use algebraic manipulations to simplify it.
Step 1: Evaluate the Exponential Terms
The first step is to evaluate the exponential terms in the expression. We have:
- 5^2x = (5^2)^x = 25^x
- 6.5^x = 6.5^x (no simplification possible)
So, the expression becomes:
25^x - 6.5^x + 1 + 125 = 0
Step 2: Combine Like Terms
Next, we will combine like terms in the expression. We have:
- 1 and 125 are constants, so we can combine them:
- 1 + 125 = 126
- 25^x and -6.5^x are exponential terms, so we cannot combine them further.
The expression becomes:
25^x - 6.5^x + 126 = 0
Final Simplification
The final simplified expression is:
25^x - 6.5^x + 126 = 0
This expression is in its simplest form. We cannot simplify it further using algebraic manipulations.
In conclusion, we have successfully simplified the expression 5^2x - 6.5^x + 1 + 125 = 0 to 25^x - 6.5^x + 126 = 0.
