1. 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.

2. 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.

3. 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…….

4. 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

5. 2. m²+ 14m + 49 =20

6. Your turn…..
3. t² + 2t + 1 = 25

7. 4. g²- 8g + 16 = 2

8. 5. y²- 12y + 36 =5

9. Your turn…..
6. w² + 16w + 64 = 18

10. 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.

11. 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

12. Ex. m² - m + c m² - m + (-½)² (m - ½)² Take half of the middle term
And ADD its SQUARE

13. 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

14. 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.

15. 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

16. 2. w² - 14w + 24 = 0

17. 3. x² - 18x + 5 = -12

18. 4. s² - 30s + 56 = -25

19. 5. x² + 7x = -12

20. 6. 3r² + 15r - 3 = 0

21. 7. p² = 2p + 5

22. 8. 4c² - 72 = 24c