4.5 Completing the Square

Front

What is the process of completing the square in a quadratic equation?

Back

Completing the square involves rewriting a quadratic equation in the form (x - p)² = q, where p and q are constants. This method helps in solving quadratic equations and understanding their properties.

Front

What is the completed square form of x² + 10x?

Back

x² + 10x + 25, which can be written as (x + 5)².

Front

How do you find the value to complete the square for x² + bx?

Back

Take half of b, square it, and add it to the equation. For example, for x² + 10x, half of 10 is 5, and 5² is 25.

Front

What is the completed square form of x² - 4x + 4?

Back

(x - 2)².

Front

How do you solve x² + 6x - 4 = 36 by completing the square?

Back

Rearrange to x² + 6x - 40 = 0, complete the square to get (x + 3)² = 49, then x = 4 or x = -10.

Front

What is the value that completes the square for x² + 6x?

Back

9, because (6/2)² = 9.

Front

What are the roots of the equation n² - 2n - 3 = 0 after completing the square?

Back

n = 3 and n = -1.

Front

What is the completed square form of x² + 10x + 25?

Back

(x + 5)².

Front

How do you factor x² - 4x + 4 = 20 using completing the square?

Back

Rewrite as (x - 2)² = 20.

Front

What is the first step in completing the square for a quadratic equation?

Back

Move the constant term to the other side of the equation.