Question

Troy was asked to rewrite the quadratic expression using the method of completing the square. She obtained (x + 6)². What number goes in the box?

Answer 1

The number that completes the square in the quadratic expression that Troy rewrote as (x + 6)² is 36.

Step-by-step explanation:

When Troy rewrote the quadratic expression as (x + 6)², to complete the square, this implies that her original quadratic equation was in the form of x² + bx + c = 0. In the expression (x + 6)², we can expand it to get x² + 12x + 36. Thus, the constant term 'c' that completes the square in the original quadratic equation is 36.

To verify, we equate the expression to zero to represent the standard quadratic equation form, which becomes x² + 12x + 36 = 0. If we were to apply the method of completing the square from an incomplete quadratic expression such as x² + 12x, we would add (6)² or 36 to complete the square, resulting in the expression Troy obtained.