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Published byEmily Hughes Modified over 3 years ago

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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.

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**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.

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**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…….

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**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

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2. m²+ 14m + 49 =20

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Your turn….. 3. t² + 2t + 1 = 25

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4. g²- 8g + 16 = 2

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5. y²- 12y + 36 =5

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Your turn….. 6. w² + 16w + 64 = 18

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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.

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**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

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**Ex. m² - m + c m² - m + (-½)² (m - ½)² Take half of the middle term**

And ADD its SQUARE

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**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

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**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.

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**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

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2. w² - 14w + 24 = 0

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3. x² - 18x + 5 = -12

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4. s² - 30s + 56 = -25

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5. x² + 7x = -12

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6. 3r² + 15r - 3 = 0

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7. p² = 2p + 5

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8. 4c² - 72 = 24c

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