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The given equation is:

\[
2(25)^{x+1} + 5^{x+2} - 3 = 0
\]

### Step-by-Step Solution:

#### Step 1: Simplify the powers of 25 and 5
Recall that \( 25 = 5^2 \). So we can rewrite \( 25^{x+1} \) as follows:

\[
25^{x+1} = (5^2)^{x+1} = 5^{2(x+1)} = 5^{2x+2}
\]

Thus, the equation becomes:

\[
2(5^{2x+2}) + 5^{x+2} - 3 = 0
\]

#### Step 2: Factor out common powers of 5
Notice that both terms involve powers of 5. Let's express them as powers of 5 and try to factor. The equation is:

\[
2 \cdot 5^{2x+2} + 5^{x+2} - 3 = 0
\]

Since \( 5^{x+2} \) is a common term, let's factor it:

\[
5^{x+2}(2 \cdot 5^x + 1) - 3 = 0
\]

#### Step 3: Solve for \( x \)
At this point, solving the equation directly might involve trial and error, logarithmic functions, or checking the possible values of \( x \).

By testing potential values, or solving further, we

Penyelesaian persamaan 2(25)^{x+1} + 5^{x+2} - 3 = 0

Learn how to solve the exponential equation 2(25)^{x+1} + 5^{x+2} - 3 = 0 with a detailed step-by-step solution. This problem covers key algebraic concepts, including exponent rules and logarithmic identities. Suitable for students in Grades 10-12.

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