5.5 Completing the Square Practice

Front

What is the process of completing the square?

Back

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial, making it easier to solve for the variable.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression of the form (a + b)² = a² + 2ab + b², which can be factored into (a + b)².

Front

How do you complete the square for the expression x² - 14x?

Back

Add (14/2)² = 49 to complete the square, resulting in (x - 7)².

Front

What is the value needed to complete the square for x² + 6x?

Back

The value is 9, since (6/2)² = 9, resulting in (x + 3)².

Front

In the equation x² = 9 - 4x, what term needs to be moved to complete the square?

Back

The term -4x needs to be moved to the left side of the equation.

Front

What is the equivalent expression for the perfect square trinomial x² + 14x + 49?

Back

The equivalent expression is (x + 7)².

Front

How do you solve the equation x² + 12x = 5 by completing the square?

Back

Rearrange to x² + 12x + 36 = 41, then factor to (x + 6)² = 41.

Front

What are the solutions to the equation x² + 12x = 5 after completing the square?

Back

The solutions are x = -6 + √41 and x = -6 - √41.

Front

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

Back

The first step is to move the constant term to the other side of the equation.

Front

What does the term 'completing the square' refer to in algebra?

Back

It refers to the process of transforming a quadratic expression into a perfect square form.