Solve (-x)² - 25: Working with Squared Negative Variables

To solve this problem, we'll proceed as follows:

• Step 1: Recognize that $(-x)^2 = x^2$.
• Step 2: Establish the equation by substituting: $x^2 - 25 = 0$.
• Step 3: Recognize this as a difference of squares: $(x - 5)(x + 5) = 0$.
• Step 4: Solve for $x$ from the factors: $x - 5 = 0$ and $x + 5 = 0$.
• Step 5: Find solutions: $x = 5$ and $x = -5$.

Therefore, the solution to the equation is $x = \pm 5$.

The correct choice among the options provided is $x = \pm 5$.