Final Answer:
For (x = -2), the expression ( -5x² - 4x - 3) evaluates to ( -5(-2)² - 4(-2) - 3 = -5(4) + 8 - 3 = -20 + 8 - 3 = -15).
Step-by-step explanation:
Given the expression ( -5x² - 4x - 3), we are tasked with evaluating it for (x = -2). Substituting (x) with (-2) in the expression, we proceed step by step following the order of operations (PEMDAS/BODMAS - Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction).
Substituting (x = -2) in the expression gives us:
( -5x² - 4x - 3 = -5(-2)² - 4(-2) - 3 = -5(4) + 8 - 3 = -20 + 8 - 3 = -15).
First, we square (-2) to get (4), then multiply by (-5) which equals (-20). Subsequently, we compute 4 times (-4) resulting in (8) and subtract (3). Finally, performing the arithmetic operations from left to right, we get the final answer, which is (-15).
Therefore, after substitution and step-by-step calculation following the order of operations, the expression evaluates to (-15) when (x = -2).