Solve ` 2(25)^(x) - 5 (10^(x))+2(4^(x)) ge 0`.

Explanation

To solve the inequality \( 2(25)^x - 5(10^x) + 2(4^x) \geq 0 \), we will follow these steps:

### Step 1: Rewrite the terms in base 5 and 2
We start by rewriting \( 25^x \), \( 10^x \), and \( 4^x \) in terms of base 5 and base 2:
- \( 25^x = (5^2)^x = 5^{2x} \)
- \( 10^x = (5 \cdot 2)^x = 5^x \cdot 2^x \)
- \( 4^x = (2^2)^x = 2^{2x} \)

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