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Day 1: Section 9 3 Solving Quadratic Equations by Completing the Square

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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. x 2 + 4x + 4 = x 2 + 2(2)x + 2 2 = (x+2) 2

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Complete the Square 1.) m 2 + 12m + 36 = m 2 + 2(6)m + 6 2 = (m + 6) 2 2.) r 2 6r + 9 = r 2 + 2(-3)r + (-3) 2 = (r 3) 2 3.) x 2 2x + 1 = x 2 + 2(-1)x + (-1) 2 = (x 1) 2

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Solve x 2 2x + 1 = 9 x 2 2x + 1 = 9 x 2 + 2(-1)x + (-1) 2 = 9 (x 1) 2 = 9 x = 3 + 1 or x = -3 + 1 x = 4 or x = -2 Solution Set: {-2, 4}

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

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1.) x 2 + 4x + 4 = 9 x 2 + 4x + 4 = 9 x 2 + 2(x)(2) + (2) 2 = 9 (x + 2) 2 = 9 x + 2 = 3 x + 2 + -2 = -2 3 x = -2 3 x = -2 + 3 x = 1 x = -2 3 x = -5 x = {-5, 1}

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

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Section 9 3 Day 2 Solving Quadratic Equations by Completing the Square

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

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Find the value of c that makes it a perfect square. x 2 + 6x + c Step 1: Step 2: (3) 2 = 9 Step 3.) c = 9 Check: x 2 + 6x + 9 = (x + 3) 2

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Find the value of c that makes it a perfect square. x 2 8x + c Step 1: Step 2: (-4) 2 = 16 Step 3.) c = 16 Check: x 2 8x + 16 = (x - 4) 2

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Solve x 2 + 6x + 3 = 10 by completing the square x 2 + 6x + 3 = 10 x 2 + 6x + 3 + -3 = 10 + -3 x 2 + 6x = 7 Since add 9 to each side x 2 + 6x + 9 = 7 + 9 x 2 + 2(x)(3) + (3) 2 = 16 (x + 3) 2 = 16 x + 3 = 4 x + 3 + -3= -3 4 x = -3 4 x = -3 + 4 x =1 x = -3 - 4 x = -7 x = {-7, 1}

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

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