Question

Use the expression x^2 + 10x − 13 to answer the following questions.Part A: What numeric expression should be added in order to complete the square for the given expression?Part B: What expression is equivalent to the given expression after completing the square?Select two answers: one for Part A and one for Part B.

Answer 1

To complete the square, add 25 to the expression x² + 10x − 13. The equivalent expression after completing the square is (x + 5)² − 38.

Step-by-step explanation:

To complete the square for the quadratic expression x² + 10x − 13, we need to form a perfect square trinomial. To do this, we take the coefficient of the x term, which is 10, divide it by 2 to get 5, and then square it to get 25.

Part A: The numeric expression that should be added to complete the square is 25 because (5)² = 25.

Part B: By adding 25 and subtracting 25 to maintain the equality of the original expression, we have x² + 10x + 25 − 25 − 13. The equivalent expression after completing the square is (x + 5)² − 38.