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Published byDouglas Wilkerson Modified over 4 years ago

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**Solving Quadratic Equations by Completing the Square**

Day 1: Section 9 – 3

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Main Ideas Solve quadratic equations by finding the square root. Solve quadratic equations by completing the square.

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**Determine if the quadratic is a perfect square.**

x2 + 4x + 4 = x2 + 2(2)x + 22 = (x+2)2

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Complete the Square 1.) m2 + 12m + 36 = m2 + 2(6)m + 62 = (m + 6)2 2.) r2 – 6r + 9 = r2 + 2(-3)r + (-3)2 = (r – 3)2 3.) x2 – 2x + 1 = x2 + 2(-1)x + (-1)2 = (x – 1)2

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Solve x2 – 2x + 1 = 9 x2 – 2x + 1 = 9 x2 + 2(-1)x + (-1)2 = 9 (x – 1)2 = 9 x = or x = x = 4 or x = -2 Solution Set: {-2, 4}

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Solve x2 – 4x + 4 = 5 x2 – 4x + 4 = 5 x2 + 2(-2)x + (-2)2 = 5 (x – 2)2 = 5 Solution Set: {-0.2, 4.2}

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**x = {-5, 1} x = -2 + 3 x = 1 x = -2 – 3 x = -5 1.) x2 + 4x + 4 = 9**

x2 + 4x + 4 = 9 x2 + 2(x)(2) + (2)2 = 9 (x + 2)2 = 9 x + 2 = ±3 x = -2 ± 3 x = -2 ± 3 x = -2 – 3 x = -5 x = {-5, 1}

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3.) x2 – 8x + 16 = 5 3.) x2 – 8x + 16 = 5 x2 – 2(x)(4) + (4)2 = 5 (x – 4)2 = 5 x ≈ {1.8, 6.2}

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**Solving Quadratic Equations by Completing the Square**

Section 9 – 3 Day 2

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Steps 1.) Find 2.) Find 3.) Add to ax2 + bx

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**Find the value of c that makes it a perfect square.**

x2 + 6x + c Step 1: Step 2: (3)2 = 9 Step 3.) c = 9 Check: x2 + 6x + 9 = (x + 3)2

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**Find the value of c that makes it a perfect square.**

x2 – 8x + c Step 1: Step 2: (-4)2 = 16 Step 3.) c = 16 Check: x2 – 8x + 16 = (x - 4)2

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**Solve x2 + 6x + 3 = 10 by completing the square**

x2 + 6x = 7 Since add 9 to each side x2 + 6x + 9 = 7 + 9 x2 + 2(x)(3) + (3)2 = 16 (x + 3)2 = 16 x + 3 = ±4 x = -3 ± 4 x = -3 ± 4 x = x =1 x = x = -7 x = {-7, 1}

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t2 – 4t + 3 = 0 t = 2 + 1 t = 3 t2 – 4t + 3 = 0 t2 – 4t = t2 – 4t = -3 t2 + 2(t)(-2) + (-2)2 = -3 + (-2)2 t2 – 4t + 4 = (t – 2)2 = 1 t – 2 = ±1 t = 2 ±1 t = 2 ±1 t = 2 - 1 t = 1 t = {1,3}

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**t = {-9,-1} y2 + 10y = -9 t = -5 + 4 t = -1 t = -5 - 4 t = -9**

y2 + 10y = -9 y2 + 2(y)(5) + (5)2 = -9 + (5)2 y2 + 10y + 25 = y2 + 10y + 25 = 16 (t + 5)2 = 16 t + 5 = ±4 t = -5 ±4 t = -5 ±4 t = t = -1 t = t = -9 t = {-9,-1}

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