Question

Complete the square for the expression. Also, identify the resulting expression as a binomial squared.

x² - 15x + ____.
A) (x - 7.5)²
B) (x - 5)²
C) (x - 7)²
D) (x - 8)²

Answer 1

To complete the square of the expression x² - 15x + ____, you must add (7.5)², which is 56.25, to the expression, resulting in (x - 7.5)². Therefore, option A is correct.

Step-by-step explanation:

To complete the square for the expression x² - 15x + ____, we need to find a constant term that allows the expression to be written as a binomial squared. The process involves taking half of the linear coefficient (which is -15 in this case), squaring it, and adding it to the expression.

Step 1: Take half of the linear coefficient, -15.

½ × (-15) = -7.5

Step 2: Square the result to find the term to complete the square.

(-7.5)² = 56.25

Step 3: Add this term to the expression to complete the square.

x² - 15x + 56.25

This results in a binomial squared that can be written as:

(x - 7.5)²

Therefore, the correct option is:

A) (x - 7.5)²