Presentation on theme: "Lesson 10.3-Solving Quadratic Equations by Completing the Square, pg. 539 Objective: To solve quadratic equations by completing the square.To solve quadratic."— Presentation transcript:
Lesson 10.3-Solving Quadratic Equations by Completing the Square, pg. 539 Objective: To solve quadratic equations by completing the square.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.
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. m ²+ 14m + 49 =20
Your turn….. 3. t² + 2t + 1 = 25
4. g ²- 8g + 16 = 2
5. y ²- 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 dont 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