Section 8 1 Completing the Square Factoring Before
Section 8. 1 Completing the Square
Factoring • Before today the only way we had for solving quadratics was to factor. Zero-factor property x 2 - 2 x - 15 = 0 (x + 3)(x - 5) = 0 x + 3 = 0 or x - 5 = 0 x = -3 or x = 5 x = {-3, 5}
Factoring x 2 = 9 x 2 - 9 = 0 Zero-factor (x + 3)(x - 3) = 0 property x + 3 = 0 or x - 3 = 0 x = -3 or x = 3 x = {-3, 3}
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.
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.
Solving Quadratic Equations by Completing the Square x 2 - 2 x Now - 15 take= 0 1/2 of the coefficient of x. Square it. = 0 (x + 3)(x - 5) Add the result to both sides. x + 3 Factor = 0 the left. Simplify the right. or x - 5 = 0 Root x. Square = -3 or x =Property 5 x = {-3, 5}
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. 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. 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. 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.
Deriving The Quadratic Formula Divide both sides by a Complete the square by adding (b/2 a)2 to both sides Factor (left) and find LCD (right) Combine fractions and take the square root of both sides Subtract b/2 a and simplify
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.
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