Simplify (-x²) + (-2½x²): Combining Like Terms with Negative Squares

To solve the problem, follow these steps:

• Step 1: Identify the coefficients of the terms involved.
• Step 2: Add the coefficients while considering their signs.
• Step 3: Write the simplified expression.

Let's break down the calculation:
Step 1: The expression given is $(-x^2) + (-2\frac{1}{2}x^2)$.
Step 2: Recognize that $-x^2$ has a coefficient of $-1$ and $-2\frac{1}{2}x^2$ has a coefficient of $-2.5$.
Step 3: Add these coefficients: $-1 + (-2.5) = -3.5$.
Therefore, the simplified expression is $-3.5x^2$.

Thus, the solution to the problem is $-3\frac{1}{2}x^2$.