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Section 8.1 Completing the Square

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Factoring Before today the only way we had for solving quadratics was to factor. x 2 - 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

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Factoring x 2 = 9 x 2 - 9 = 0 (x + 3)(x - 3) = 0 x + 3 = 0 or x - 3 = 0 x = -3 or x = 3 x = {-3, 3} Zero-factor property

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

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

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

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

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Solve each equation. Write radicals in simplified form.

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Solving Quadratic Equations by Completing the Square x 2 - 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

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Completing the Square 1. Divide by the coefficient of the squared term. 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.

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Completing the Square 1. Divide by the coefficient of the squared term. 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.

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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.

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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.

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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.

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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

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

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