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.