Chapter 10 Quadratic Equations Section 1 Solving Quadratic

Study Strategy Study Groups üKeeping Track Copyright © 2016, 2012, and 2009 Pearson Education,

Concept Solving a Quadratic Equation by Factoring 1. Write the equation in standard form:

Example 1 Solve: Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 5

Concept Solving a Quadratic Equation by Extracting Square Roots 1. Isolate the squared term.

Example Solving a Quadratic Equation by 2 Extracting Square Roots Solve: Copyright © 2016,

Example Solve x 2 = – 60. 3 x 2 = – 60 The

Example Solving a Quadratic Equation by Extracting Square Roots 4 Solve: Copyright © 2016,

Concept Solving a Quadratic Equation by Completing the Square 1. Isolate all variable terms

Example Solving a Quadratic Equation by Completing the Square (page 1) 5 Solve by

Example Solving a Quadratic Equation by Completing the Square (page 2) Copyright © 2016,

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Concept Solving a Quadratic Equation by Factoring 1. Write the equation in standard form: 2. Completely factor the quadratic expression. 3. Set each factor equal to 0 and solve. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 3

Example Solve x 2 – 7 x = – 12 x 2 – 7 x + 12 = 0 Collect all terms on the left side. (x – 3)(x – 4) = 0 Factor. x– 3=0 or x – 4 = 0 Set each factor equal to 0. x=3 or x=4 The solution set is {3, 4}. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 4

Concept Solving a Quadratic Equation by Extracting Square Roots 1. Isolate the squared term. 2. Take the square root of each side. (Remember when taking the square root of the constant. ) 3. Simplify the square root. 4. Solve the resulting equation. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 6

Concept Solving a Quadratic Equation by Completing the Square 1. Isolate all variable terms on one side of the equation, with the constant term on the other side of the equation. 2. If the coefficient of the second-degree term is not equal to 1, then divide both sides of the equation by that coefficient. 3. Identify the coefficient of the first-degree term. Take half of that number, square it, and add that to both sides of the equation. 4. Factor the resulting perfect square trinomial. 5. Take the square root of each side of the equation. Be sure to include on the side where the constant is. 6. Solve the resulting equation. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 10

Example 6 Solve x 2 – 6 x + 11 = 0. x 2 – 6 x = – 11 x 2 – 6 x + 9 = – 11 + 9 x 2 – 6 x + 9 = – 2 (x – 3)2 = – 2 Subtract 11. (6/2)2 = (3)2 = 9 Simplify. The solution set is Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 13