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**9.4 – Solving Quadratic Equations By Completing The Square**

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Ex. 1 a. Solve x2 – 12x + 36 = 0.

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Ex. 1 a. Solve x2 – 12x + 36 = 0. x2 – 12x + 36 = 0

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Ex. 1 a. Solve x2 – 12x + 36 = 0. x2 – 12x + 36 = 0 (x )(x ) = 0

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Ex. 1 a. Solve x2 – 12x + 36 = 0. x2 – 12x + 36 = 0 (x – 6)(x – 6) = 0

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Ex. 1 a. Solve x2 – 12x + 36 = 0. x2 – 12x + 36 = 0 (x – 6)(x – 6) = 0 (x – 6)2 = 0

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Ex. 1 a. Solve x2 – 12x + 36 = 0. x2 – 12x + 36 = 0 (x – 6)(x – 6) = 0 √(x – 6)2 = √0

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Ex. 1 a. Solve x2 – 12x + 36 = 0. x2 – 12x + 36 = 0 (x – 6)(x – 6) = 0 √(x – 6)2 = √0 x – 6 = 0

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Ex. 1 a. Solve x2 – 12x + 36 = 0. x2 – 12x + 36 = 0 (x – 6)(x – 6) = 0 √(x – 6)2 = √0 x – 6 = 0 x = 6

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b. Solve x2 + 8x + 16 = 0.

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b. Solve x2 + 8x + 16 = 0. x2 + 8x + 16 = 0 (x + 4)(x + 4) = 0 √(x + 4)2 = √ 0 x + 4 = 0 x = -4

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b. Solve x2 + 8x + 16 = 0. x2 + 8x + 16 = 0 (x + 4)(x + 4) = 0 (x + 4)2 = 0 x + 4 = 0 x = -4 Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square.

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b. Solve x2 + 8x + 16 = 0. x2 + 8x + 16 = 0 (x + 4)(x + 4) = 0 (x + 4)2 = 0 x + 4 = 0 x = -4 Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square. x2 + 10x + 21 = 0

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b. Solve x2 + 8x + 16 = 0. x2 + 8x + 16 = 0 (x + 4)(x + 4) = 0 (x + 4)2 = 0 x + 4 = 0 x = -4 Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square. x2 + 10x + 21 = 0 Want x2 + 10x + 25

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b. Solve x2 + 8x + 16 = 0. x2 + 8x + 16 = 0 (x + 4)(x + 4) = 0 (x + 4)2 = 0 x + 4 = 0 x = -4 Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square. x2 + 10x + 21 = 0 x2 + 10x + 25 = 4

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b. Solve x2 + 8x + 16 = 0. x2 + 8x + 16 = 0 (x + 4)(x + 4) = 0 (x + 4)2 = 0 x + 4 = 0 x = -4 Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square. x2 + 10x + 21 = 0 x2 + 10x + 25 = 4 (x + 5)2 = 4

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b. Solve x2 + 8x + 16 = 0. x2 + 8x + 16 = 0 (x + 4)(x + 4) = 0 (x + 4)2 = 0 x + 4 = 0 x = -4 Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square. x2 + 10x + 21 = 0 x2 + 10x + 25 = 4 (x + 5)2 = 4 x + 5 = ±2

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b. Solve x2 + 8x + 16 = 0. x2 + 8x + 16 = 0 (x + 4)(x + 4) = 0 (x + 4)2 = 0 x + 4 = 0 x = -4 Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square. x2 + 10x + 21 = 0 x2 + 10x + 25 = 4 (x + 5)2 = 4 x + 5 = ±2 x + 5 = 2

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b. Solve x2 + 8x + 16 = 0. x2 + 8x + 16 = 0 (x + 4)(x + 4) = 0 (x + 4)2 = 0 x + 4 = 0 x = -4 Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square. x2 + 10x + 21 = 0 x2 + 10x + 25 = 4 (x + 5)2 = 4 x + 5 = ±2 x + 5 = 2 x + 5 = -2

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b. Solve x2 + 8x + 16 = 0. x2 + 8x + 16 = 0 (x + 4)(x + 4) = 0 (x + 4)2 = 0 x + 4 = 0 x = -4 Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square. x2 + 10x + 21 = 0 x2 + 10x + 25 = 4 (x + 5)2 = 4 x + 5 = ±2 x + 5 = 2 x + 5 = -2 x = -3

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b. Solve x2 + 8x + 16 = 0. x2 + 8x + 16 = 0 (x + 4)(x + 4) = 0 (x + 4)2 = 0 x + 4 = 0 x = -4 Ex. 2 a. Solve x2 + 10x + 21 = 0 by completing the square. x2 + 10x + 21 = 0 x2 + 10x + 25 = 4 (x + 5)2 = 4 x + 5 = ±2 x + 5 = 2 x + 5 = -2 x = x = -7

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**b. Solve x2 + 14x = 12 by completing the square.**

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**b. Solve x2 + 14x = 12 by completing the square.**

Want x2 + 14x + 49 x2 + 14x + 49 = 61 (x + 7)2 = 61 x + 7 = ±√61 x = -7 ± √61 x ≈ 0.8 or x ≈ -14.8

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