To solve the equation:

\[
-\sqrt{25x} + 8 = -2
\]

we'll go step by step:

### Step 1: Isolate the square root term
Subtract 8 from both sides to isolate the square root term:

\[
-\sqrt{25x} = -2 - 8
\]

\[
-\sqrt{25x} = -10
\]

### Step 2: Eliminate the negative sign
Multiply both sides by -1 to eliminate the negative sign:

\[
\sqrt{25x} = 10
\]

### Step 3: Square both sides
Square both sides of the equation to get rid of the square root:

\[
25x = 10^2
\]

\[
25x = 100
\]

### Step 4: Solve for \( x \)
Divide both sides by 25:

\[
x = \frac{100}{25}
\]

\[
x = 4
\]

### Final Answer:
The solution to the equation is \( x = 4 \).

Would you like more details on this solution or have any questions?

Here are five related questions you might find helpful:
1. How do you solve equations involving cube roots?
2. What happens if there are multiple square root terms in an equation?
3. How do you solve an equation like \( \sqrt{x+1} + 3 = 7 \)?
4. How do you solve equations involving fractional exponents?
5. What are the steps to check your solution when dealing with square roots?

**Tip:** Always check for extraneous solutions when solving equations involving square roots, as squaring both sides can introduce non-valid solutions.

Learn how to solve the equation -√25x + 8 = -2 with a detailed, step-by-step breakdown. This solution covers algebraic manipulation, properties of square roots, and solving for x. Suitable for students in Grades 8-10.

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