Lesson 10.3-Solving Quadratic Lesson 10.3-Solving Quadratic Equations by Completing the Equations by Completing the Square, pg. 539Square, pg. 539

Lesson 10.3-Solving Quadratic Lesson 10.3-Solving Quadratic Equations by Completing the Equations by Completing the Square, pg. 539Square, pg. 539

Objective:Objective:•To solve quadratic equations by To solve quadratic equations by completing the square.completing the square.

Finding the Square RootSome equations can be solved by taking

the square root of each side.

Square Root Symbol: √

To solve an equation by taking the square root, you must rewrite the perfect square trinomials as a binomial square.

Reminder……..Perfect Square Trinomialsa²+ 2ab + b² = (a + b)²a² - 2ab + b²= (a – b) ²

Perfect Squares:1, 4, 9, 16, 25, 36, 49, 64, 81, 100,

121, 144, 169, 196, 225…….

Ex. 1: Solve each equation by taking the square root of each side. Round to the nearest tenth if necessary.

1. b² - 6b + 9 = 25

2. m²+ 14m + 49 =20

Your turn…..3. t² + 2t + 1 = 25

4. g²- 8g + 16 = 2

5. y²- 12y + 36 =5

Your turn…..6. w² + 16w + 64 = 18

Ex. p²+ 12p = 13

When solving a quadratic equation using the Square Root property you must have a Perfect Square Trinomial. If you don’t then you must create one.

Creating a Perfect Square Trinomial

Ex. x²+ 6x + c x²+ 6x + 3² x² + 6x + 9 (x + 3)²

Take half of the middle term And ADD its SQUARE

Ex. m² - m + c m² - m + (-½)² (m - ½)²

Take half of the middle term And ADD its SQUARE

Try these…. Find the value that makes each trinomial a perfect square. Then write the binomial square.

1. t² - 24t + c

2. b² + 28b + c

3. y² + 40y + c

4. g² - 9g + c

This method is called Completing the Square

Steps for Completing the Square

Step 1: Make sure the leading coefficient is ONE, if not, DIVIDE the entire equation by the leading coefficient.

Step 2: Isolate the variable terms ax² + bx Step 3: Find b/2 and ADD its square to both sides.

Step 4: Solve by using the SQUARE ROOT PROPERTY.

Ex. 2: Solve each equation by completing the square. Round to the nearest tenth if necessary.

1. x² + 6x + 3 = 0

2. w² - 14w + 24 = 0

3. x² - 18x + 5 = -12

4. s² - 30s + 56 = -25

5. x² + 7x = -12

6. 3r² + 15r - 3 = 0

7. p² = 2p + 5

8. 4c² - 72 = 24c