Completing the square

Front

What is 'completing the square'?

Back

Completing the square is a method used to solve quadratic equations by rewriting them in the form (x + p)² = q, making it easier to find the roots.

Front

How do you complete the square for the equation x² + 12x = 5?

Back

1. Move 5 to the other side: x² + 12x - 5 = 0. 2. Take half of 12 (which is 6), square it (36), and add to both sides: x² + 12x + 36 = 41. 3. Rewrite as (x + 6)² = 41.

Front

What do you add to complete the square for x² + 6x?

Back

To complete the square, add (6/2)² = 9, so x² + 6x + 9 = (x + 3)².

Front

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

Back

The completed square form is (x + 5)² - 25.

Front

What is the formula to find the number to add when completing the square?

Back

The number to add is (b/2)², where b is the coefficient of x in the quadratic equation ax² + bx + c.

Front

Solve by completing the square: x² + 14x + ____. What do you add?

Back

Add 49 to complete the square: x² + 14x + 49 = (x + 7)².

Front

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

Back

The completed square form is (x + 5)².

Front

How do you solve x² + 6x = 20 by completing the square?

Back

1. Move 20 to the other side: x² + 6x - 20 = 0. 2. Add (6/2)² = 9 to both sides: x² + 6x + 9 = 29. 3. Rewrite as (x + 3)² = 29.

Front

What is the solution to x² + 12x = 5 after completing the square?

Back

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

Front

What do you need to add to complete the square for x² + 10x = 25?

Back

You need to add 25 to complete the square: x² + 10x + 25 = (x + 5)².