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

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Objective: To solve quadratic equations by completing the square.
Lesson 10.3-Solving Quadratic Equations by Completing the Square, pg. 539 Objective: To solve quadratic equations by completing the square.

Finding the Square Root
Some 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 Trinomials a²+ 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
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

Try these…. Find the value that makes each trinomial a perfect square
Try these…. Find the value that makes each trinomial a perfect square. Then write the binomial square. t² - 24t + c 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
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