Factoring x2 - 9 = 0 (x + 3)(x - 3) = 0 x + 3 = 0 or x - 3 = 0 Zero-factor property

Another Way to Solve Quadratics Square Root Property Recall that we know the solution set is x = {-3, 3} When you introduce the radical you must use + and - signs.

Solving Quadratic Equations by Completing the Square Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation

Perfect Square Trinomials Create perfect square trinomials. x2 + 20x + ___ x2 - 4x + ___ x2 + 5x + ___ 100 4 25/4

Creating a Perfect Square Trinomial In the following perfect square trinomial, the constant term is missing. X2 + 14x + ____ Find the constant term by squaring half the coefficient of the linear term. (14/2)2 X2 + 14x + 49

Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.

Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side

Solving Quadratic Equations by Completing the Square Step 5: Set up the two possibilities and solve

Solving Quadratic Equations by Completing the Square

Section 8.1 Completing the Square

Factoring (x + 3)(x - 5) = 0 x + 3 = 0 or x - 5 = 0 x = -3 or x = 5 Before today the only way we had for solving quadratics was to factor. x2 - 2x - 15 = 0 (x + 3)(x - 5) = 0 x + 3 = 0 or x - 5 = 0 x = -3 or x = 5 x = {-3, 5} Zero-factor property

OR Square Root Property If x and b are complex numbers and if x 2 = b, then OR

Solve each equation. Write radicals in simplified form. Square Root Property

Solve each equation. Write radicals in simplified form. Square Root Property Radical will not simplify.

HW Requests: pg 303 #42-49; Pg 310 #15-37 odds AAT-A Date: 2/5/14 SWBAT complete the square to solve factoring problems Do Now: HW Requests: pg 303 #42-49; Pg 310 #15-37 odds In Class: Start Completing the Square WS HW: Complete WS KutaSoftware 1-24 odds Begin Section 6.5 Announcements: Tutoring: Tues. and Thurs. 3-4 Bring Graphing Calculator to Class for Thursday Quiz Friday w/HW Quiz before Complete presentations Life Is Just A Minute Life is just a minute—only sixty seconds in it. Forced upon you—can't refuse it. Didn't seek it—didn't choose it. But it's up to you to use it. You must suffer if you lose it. Give an account if you abuse it. Just a tiny, little minute, But eternity is in it! By Dr. Benjamin Elijah Mays, Past President of Morehouse College

Homework Quiz Solve each equation by factoring. 3x2 =5x

Homework Quiz Solve each equation by factoring. 3x2 =5x x= {0, 5/3}

Solving Quadratic Equations by Completing the Square Try the following examples. Do your work on your paper and then check your answers.

Solve each equation. Write radicals in simplified form. Square Root Property Solution Set

Solve each equation. Write radicals in simplified form.

Solve each equation. Write radicals in simplified form.

Perfect Square Trinomials Examples x2 + 6x + 9 x2 - 10x + 25 x2 + 12x + 36

1. Divide by the coefficient of the squared term 1. Divide by the coefficient of the squared term. Make the coefficient of the squared term =1. 2. Move all variables to one side and constants to the other. 3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation. 4. Factor the left hand side and simplify the right. 5. Root and solve. Completing the Square

1. Divide by the coefficient of the squared term 1.Divide by the coefficient of the squared term. Make the coefficient of the squared term =1. 2. Move all variables to one side and constants to the other. 3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation. 4. Factor the left hand side and simplify the right. 5. Root and solve. Completing the Square

Completing the Square 1. Make the coefficient of the squared term =1. 2. Move all variables to one side and constants to the other. 3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation. 4. Factor the left hand side and simplify the right. 5. Root and solve. Completing the Square

1. Divide by the coefficient of the squared term 1.Divide by the coefficient of the squared term. Make the coefficient of the squared term =1. 2. Move all variables to one side and constants to the other. 3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation. 4. Factor the left hand side and simplify the right. 5. Root and solve. Completing the Square

1. Make the coefficient of the squared term =1. 2. Move all variables to one side and constants to the other. 3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation. 4. Factor the left hand side and simplify the right. 5. Root and solve.

Solving Quadratic Equations by Completing the Square x2 - 2x - 15 = 0 (x + 3)(x - 5) = 0 x + 3 = 0 or x - 5 = 0 x = -3 or x = 5 x = {-3, 5} Now take 1/2 of the coefficient of x. Square it. Add the result to both sides. Factor the left. Simplify the right. Square Root Property

Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.

Deriving The Quadratic Formula Divide both sides by a Complete the square by adding (b/2a)2 to both sides Factor (left) and find LCD (right) Combine fractions and take the square root of both sides Subtract b/2a and simplify

Completing the Square-Example #2 Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation, the constant to the right side of the equation.

Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides. The quadratic coefficient must be equal to 1 before you complete the square, so you must divide all terms by the quadratic coefficient first.

Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.

Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side