Download presentation

Published byEmily Hughes Modified over 7 years ago

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

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google