Squarely brought to you squares by Completing the Square Squarely brought to you squares by Mr. Peter Richard (Who is not a square)

Many quadratic equations contain expressions that cannot be easily factored. For equations containing these types of expressions, you can use square roots to find the roots. Sometimes you may have to round the roots, so they are no longer square roots, they are rounded roots!

Perfect Square Trinomials Examples x2 + 6x + 9 x2 - 10x + 25 x2 + 12x + 36

Creating a Perfect Square Trinomial In the following perfect square trinomial, the constant term is missing. X2 + 14x + ____ Find the constant term by squaring half the coefficient of the linear term. (14/2)2 X2 + 14x + 49

Perfect Square Trinomials Create perfect square trinomials. x2 + 20x + ___ x2 - 4x + ___ x2 + 5x + ___ 100 4 25/4

Solving Quadratic Equations by Completing the Square Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation

Solving Quadratic Equations by Completing the Square Step 2: Take half of the middle (B) term. Square it, and add it to both sides of the equal sign.

Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation. (x+4)(x+4) = 36 (x + 3)2 ( + 3)(x + 3) or (x + 3)2

Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side

Solving Quadratic Equations by Completing the Square Step 5: Solve both equations

To complete the square of the expression x2 + bx, add

Example. x2 – 8x Add x2 – 8x + = (x – 4)2 = x2 – 8x + 16

Ex. x2 + 10x = 24 x2 + 10x = 24 + 52 + 52 Add to both sides x2 + 10x + 25 = 49 Find the square root of both sides (x + 5)2 = 49 x + 5 = x = 2 or x = -12

Ex. x2 – 2x – 3 = 0 x² - 2x = 3 x² -2x + = 3 + (x – 1)² = 4 X – 1 = ±2 X = 3 or -1

Ex: 2x² + 7x + 3 = 0 Do this one yourself so that you know that I know that you know how to do it!

Quiz & Homework Quiz: Page 285 # 2, 4, 6, 14, 17