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Ex. 1 Solve by factoring. 2x 2 + 9x + 7 = 0 6x 2 – 3x = 0

Ex. 1 Solve by factoring. 2x 2 + 9x + 7 = 0 6x 2 – 3x = 0. (2x + 1)(x + 4) = 0. 2x + 1 = 0 x + 4 = 0. x = - ½ x = - 4. 3x(2x – 1) = 0. 3x = 0 2x – 1 = 0. x = 0 x = ½. Ex. 2 Solve by extracting square roots. A. 4x 2 = 12.

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Ex. 1 Solve by factoring. 2x 2 + 9x + 7 = 0 6x 2 – 3x = 0

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  1. Ex. 1 Solve by factoring. 2x2 + 9x + 7 = 0 6x2 – 3x = 0 (2x + 1)(x + 4) = 0 2x + 1 = 0 x + 4 = 0 x = - ½ x = - 4 3x(2x – 1) = 0 3x = 0 2x – 1 = 0 x = 0 x = ½

  2. Ex. 2 Solve by extracting square roots A. 4x2 = 12 B. (x - 2)2 = 5 x2 = 3 Ex. 3 Completing the Square x2 - 6x + 2 = 0 First, take 2 to the other side. x2 - 6x = -2 To complete the square take half the x-term and square it. Add it to both sides. x2 - 6x = -2 + 9 + 9 (x - 3)2 = 7

  3. Ex. 4 Completing the Square when the leading coefficient is not 1 Divide each term by 3. Take 5/3 to the other side. Now, complete the square. Take the square root of both sides.

  4. Ex. 7 Use the Quadratic Formula to solve x2 + 3x - 9 = 0

  5. Ex. 8 Solve by factoring. x4 - 3x2 + 2 = 0 Factor Set both factors = 0 or factor again. (x2 - 2)(x2 - 1) = 0 x2 - 2 = 0 x2 = 2 x2 - 1 = 0 x2 = 1

  6. Ex. 9 Solve by grouping. x3 - 3x2 - 3x + 9 = 0 x2(x - 3) - 3(x - 3) = 0 Factor out an (x - 3) (x - 3)(x2 - 3) = 0 x = 3

  7. Ex. 10 Solving a Radical Isolate the radical. Now square both sides. 2x + 7 = x2 + 4x + 4 0 = x2 + 2x - 3 Factor or use quad. formula 0 = (x + 3)(x - 1) Possible answers for x are - 3 and 1. Check them in the original equation to see if they work. Only x = 1 works!

  8. Ex. 11 An equation Involving Two Radicals Isolate the more complicated rad. Square both sides. Once again, isolate the radical. Square both sides. x2 + 2x + 1 = 4(x + 4) (x - 5)(x + 3) = 0 x2 - 2x - 15 = 0 Only x = 5 works.

  9. Ex. 12 Solving an Equation Involving Absolute Value Split into 2 equations. x2 - 3x = -4x + 6 x2 - 3x = 4x -6 Now solve them for x. x2 + x - 6 = 0 x2 - 7x + 6 = 0 (x + 3)(x - 2) = 0 (x - 1)(x - 6) = 0 Possible answers are -3, 2, 1, and 6. Which ones work? -3 and 1

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