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Solving Equations by Factoring Module 8, Lesson 6 Online Algebra VHS@PWCS Solving Quadratic Equations So far we have solved quadratic equations by: 1. Taking the square root of both sides. We can do this when the equation is of the form ax2 + c = 0. Note that the only variable in this type is squared. 2. The quadratic formula. We can use this to solve any quadratic equations. b b 2 4ac x 2a Solve the following equations x2 = 25 x2 - 63 = 81 Take the square root of Get the x2 by itself. both sides. x2 – 63 + 63 = 81 + 63 x=5 x2 = 144 x = -5 Take the square root of Remember that both sides. quadratics can have 2 x = 12 solutions! x = -12 Solve the following equation. Use the quadratic formula. 2y2 + 3 = -7y 7 7 2 4(2)(3) x 2(2) 1. Get everything on the same side. 7 49 24 2y2 + 7y + 3 = -7y + 7y x 4 2y2 + 7y + 3 = 0 7 25 2. Identify a, b and c. x 4 a = 2, b = 7 and c = 3 7 5 3. Substitute into the quadratic formula. x 4 b b 2 4ac x 3 x 1 2a x 2 Zero Product Property The Zero Product Property states that: For all numbers a and b, if ab = 0, then a = 0, b= 0 or both a and b equal 0. This makes sense since 0 times any number will always give you zero. We are going to use this property to solve quadratic equations by factoring. Solve the following equation. (y + 2)(3y + 5) = 0 According to the zero product property either (y + 2) or (3y + 5) must equal zero. We will assume that each equals zero and set them equal to zero. y+2=0 3y + 5 = 0 Then we will solve. y + 2 – 2 = 0 + -2 3y + 5 + -5 = 0 + -5 y = -2 3y = -5 y = -5/3 Solve the following equation. y(y – 12) = 0 1. Set each factor equal to zero. y=0 y – 12 = 0 2. Solve. y=0 y – 12 + 12 = 0 + 12 y = 12. Remember quadratics can have 2 solutions. Solving equations by factoring Sometimes we need to factor an equation before setting it equal to zero. Solve m2 + 36m = 0 1. Factor. Here we can pull out the GCF of m. m(m + 36) = 0 2. Set each factor equal to zero. m=0 m + 36 = 0 3. Solve. m=0 m + 36 + -36 = 0 + -36 m = -36 4. We have 2 solutions m = 0 and m = -36. Solve: a2 + 4a = 21 1. Just like when using the a2 + 4a = 21 quadratic formula, we need a2 + 4a + -21 = 21 + -21 one side to be zero. a2 + 4a – 21 = 0 2. Factor 3. Set both factors equal to (a + 7)(a – 3) = 0 zero. 4. Solve a+7=0 a–3=0 a=3 a = -7 Try these! Click for the answers. c – 17c + 60 = 0 2 (c -12)(c – 5) = 0 1. c2 – 17c + 60 = 0 c – 12 = 0 c–5=0 c = 12 c=5 2. a2 + 64 = -16a a2 + 64 = -16a a2 + 64 + 16 a = -16a + 16a Since these factors are the same a2 + 16a + 64 = 0 we only need to set one equal to zero. This quadratic will have only (a + 8)(a + 8) = 0 one solution. a = -8 a+8=0 a = -8 Solving Quadratics We now have 3 different ways to solve quadratic equations. Taking the square root of both sides. This only works when the equation is of the form ax2 + c = 0. The quadratic formula This can be used with any quadratic equation. By factoring and setting factors equal to zero.

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posted: | 11/14/2011 |

language: | English |

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