Solving Quadratic
    Equations
    Module 10 - Topic 4
         PART 2
Solving Quadratic Equations when they
         do NOT equal ZERO
• So far all the quadratic equations we’ve solve have
  b...
Page 1 - Finish it
• Solve.       x − 3x − 18 = 0
                2
Page 1 - Finish it
• Solve.       x − 3x − 18 = 0
                 2



               ( x + 3) ( x − 6 ) = 0
Page 1 - Finish it
• Solve.        x − 3x − 18 = 0
                 2



               ( x + 3) ( x − 6 ) = 0
           ...
Page 1 - Finish it
• Solve.        x − 3x − 18 = 0
                 2



               ( x + 3) ( x − 6 ) = 0
           ...
Page 1 - Finish it
• Solve.        x − 3x − 18 = 0
                 2



               ( x + 3) ( x − 6 ) = 0
           ...
Page 1 - Finish it
• Solve.        x − 3x − 18 = 0
                 2



               ( x + 3) ( x − 6 ) = 0
           ...
Page 1 - Your Turn
• Solve.     x + 7x = 170
              2
Page 1 - Your Turn
• Solve.     x + 7x = 170
              2

              −170   −170
Page 1 - Your Turn
• Solve.     x + 7x = 170
                 2

                 −170   −170

            x + 7x − 170 = ...
Page 1 - Your Turn
• Solve.        x + 7x = 170
                   2

                   −170       −170

              x ...
Page 1 - Your Turn
• Solve.        x + 7x = 170
                   2

                   −170       −170

              x ...
Page 1 - Your Turn
• Solve.        x + 7x = 170
                   2

                   −170       −170

              x ...
Page 1 - Your Turn
• Solve.        x + 7x = 170
                   2

                   −170       −170

              x ...
Page 1 - Your Turn
• Solve.        x + 7x = 170
                   2

                   −170       −170

              x ...
Page 2 - Finish it
• Solve.   2x − 5x − 3 = 0
             2
Page 2 - Finish it
• Solve.     2x − 5x − 3 = 0
                2



           ( 2x + 1) ( x − 3) = 0
Page 2 - Finish it
• Solve.     2x − 5x − 3 = 0
                2



           ( 2x + 1) ( x − 3) = 0
      2x + 1 = 0   ...
Page 2 - Finish it
• Solve.     2x − 5x − 3 = 0
                2



           ( 2x + 1) ( x − 3) = 0
      2x + 1 = 0   ...
Page 2 - Finish it
• Solve.     2x − 5x − 3 = 0
                2



           ( 2x + 1) ( x − 3) = 0
      2x + 1 = 0   ...
Page 2 - Finish it
• Solve.       2x − 5x − 3 = 0
                 2



           ( 2x + 1) ( x − 3) = 0
      2x + 1 = 0...
Page 2 - Finish it
• Solve.       2x − 5x − 3 = 0
                 2



           ( 2x + 1) ( x − 3) = 0
      2x + 1 = 0...
Page 2 - Finish it
• Solve.       2x − 5x − 3 = 0
                 2



           ( 2x + 1) ( x − 3) = 0
      2x + 1 = 0...
Page 2 - Your Turn
• Solve.    11x + 6 − 10x = 0
                        2
Page 2 - Your Turn
• Solve.     11x + 6 − 10x = 02


             (
           −1 11x + 6 − 10x   2
                      ...
Page 2 - Your Turn
• Solve.     11x + 6 − 10x = 02


             (
           −1 11x + 6 − 10x   2
                      ...
Page 2 - Your Turn
• Solve.     11x + 6 − 10x = 02


             (
           −1 11x + 6 − 10x   2
                      ...
Page 2 - Your Turn
• Solve.     11x + 6 − 10x = 02


             (
           −1 11x + 6 − 10x   2
                      ...
Page 2 - Your Turn
• Solve.     11x + 6 − 10x = 02


             (
           −1 11x + 6 − 10x   2
                      ...
Page 2 - Your Turn
• Solve.     11x + 6 − 10x = 02


             (
           −1 11x + 6 − 10x   2
                      ...
Page 2 - Your Turn
• Solve.     11x + 6 − 10x = 02


             (
           −1 11x + 6 − 10x   2
                      ...
Page 2 - Your Turn
• Solve.        11x + 6 − 10x = 02


             (
           −1 11x + 6 − 10x      2
                ...
Page 2 - Your Turn
• Solve.        11x + 6 − 10x = 02


             (
           −1 11x + 6 − 10x      2
                ...
Page 2 - Your Turn
• Solve.        11x + 6 − 10x = 02


             (
           −1 11x + 6 − 10x      2
                ...
Page 3 - Your Turn
• Solve.    −16x = −4x   3
Page 3 - Your Turn
• Solve.      −16x = −4x    3

           +4x 3    +4x 3
Page 3 - Your Turn
• Solve.      −16x = −4x     3

           +4x 3     +4x 3
           4x − 16x = 0
              3
Page 3 - Your Turn
• Solve.      −16x = −4x           3

           +4x 3           +4x 3
           4x − 16x = 0
        ...
Page 3 - Your Turn
• Solve.       −16x = −4x           3

            +4x 3           +4x 3
            4x − 16x = 0
     ...
Page 3 - Your Turn
• Solve.       −16x = −4x           3

            +4x 3           +4x 3
            4x − 16x = 0
     ...
Page 3 - Your Turn
• Solve.       −16x = −4x            3

            +4x 3            +4x 3
            4x − 16x = 0
   ...
Page 3 - Your Turn
• Solve.       −16x = −4x            3

            +4x 3            +4x 3
            4x − 16x = 0
   ...
Page 3 - Your Turn
• Solve.       −16x = −4x            3

            +4x 3            +4x 3
            4x − 16x = 0
   ...
Do you want to Play a GAME?
• Check your knowledge on solving Quadratic
  Equations by playing Jeopardy. Ok, technically i...
Fantastic Job!
• You’ve finished reviewing Solving Quadratic
  Equations Part 2.

• Exit and proceed
  to the Mastery
  Ass...
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Topic 4 solving quadratic equations part 2

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Topic 4 solving quadratic equations part 2

  1. 1. Solving Quadratic Equations Module 10 - Topic 4 PART 2
  2. 2. Solving Quadratic Equations when they do NOT equal ZERO • So far all the quadratic equations we’ve solve have been equal to zero but not all are so nice. If they don’t equal zero, make them equal to zero! • View this Cool Math website to how to solve Quadratic Equations when the original equation is not equal to 0. • There are 3 pages to view. • Complete the Your Turn problems in your notebook and check your answers on the next slide.
  3. 3. Page 1 - Finish it • Solve. x − 3x − 18 = 0 2
  4. 4. Page 1 - Finish it • Solve. x − 3x − 18 = 0 2 ( x + 3) ( x − 6 ) = 0
  5. 5. Page 1 - Finish it • Solve. x − 3x − 18 = 0 2 ( x + 3) ( x − 6 ) = 0 x+3= 0 or x−6=0
  6. 6. Page 1 - Finish it • Solve. x − 3x − 18 = 0 2 ( x + 3) ( x − 6 ) = 0 x+3= 0 or x−6=0 −3 −3 +6 +6
  7. 7. Page 1 - Finish it • Solve. x − 3x − 18 = 0 2 ( x + 3) ( x − 6 ) = 0 x+3= 0 or x−6=0 −3 −3 +6 +6 x = −3 or x=6
  8. 8. Page 1 - Finish it • Solve. x − 3x − 18 = 0 2 ( x + 3) ( x − 6 ) = 0 x+3= 0 or x−6=0 −3 −3 +6 +6 x = −3 or x=6 Answer: {−3, 6}
  9. 9. Page 1 - Your Turn • Solve. x + 7x = 170 2
  10. 10. Page 1 - Your Turn • Solve. x + 7x = 170 2 −170 −170
  11. 11. Page 1 - Your Turn • Solve. x + 7x = 170 2 −170 −170 x + 7x − 170 = 0 2
  12. 12. Page 1 - Your Turn • Solve. x + 7x = 170 2 −170 −170 x + 7x − 170 = 0 2 ( x + 17 ) ( x − 10 ) = 0
  13. 13. Page 1 - Your Turn • Solve. x + 7x = 170 2 −170 −170 x + 7x − 170 = 0 2 ( x + 17 ) ( x − 10 ) = 0 x + 17 = 0 or x − 10 = 0
  14. 14. Page 1 - Your Turn • Solve. x + 7x = 170 2 −170 −170 x + 7x − 170 = 0 2 ( x + 17 ) ( x − 10 ) = 0 x + 17 = 0 or x − 10 = 0 −17 −17 +10 +10
  15. 15. Page 1 - Your Turn • Solve. x + 7x = 170 2 −170 −170 x + 7x − 170 = 0 2 ( x + 17 ) ( x − 10 ) = 0 x + 17 = 0 or x − 10 = 0 −17 −17 +10 +10 x = −17 or x = 10
  16. 16. Page 1 - Your Turn • Solve. x + 7x = 170 2 −170 −170 x + 7x − 170 = 0 2 ( x + 17 ) ( x − 10 ) = 0 x + 17 = 0 or x − 10 = 0 −17 −17 +10 +10 x = −17 or x = 10 Answer: {−17,10}
  17. 17. Page 2 - Finish it • Solve. 2x − 5x − 3 = 0 2
  18. 18. Page 2 - Finish it • Solve. 2x − 5x − 3 = 0 2 ( 2x + 1) ( x − 3) = 0
  19. 19. Page 2 - Finish it • Solve. 2x − 5x − 3 = 0 2 ( 2x + 1) ( x − 3) = 0 2x + 1 = 0 or x−3= 0
  20. 20. Page 2 - Finish it • Solve. 2x − 5x − 3 = 0 2 ( 2x + 1) ( x − 3) = 0 2x + 1 = 0 or x−3= 0 −1 −1 +3 +3
  21. 21. Page 2 - Finish it • Solve. 2x − 5x − 3 = 0 2 ( 2x + 1) ( x − 3) = 0 2x + 1 = 0 or x−3= 0 −1 −1 +3 +3 2x = −1 or x=3
  22. 22. Page 2 - Finish it • Solve. 2x − 5x − 3 = 0 2 ( 2x + 1) ( x − 3) = 0 2x + 1 = 0 or x−3= 0 −1 −1 +3 +3 2x = −1 or x=3 2 2
  23. 23. Page 2 - Finish it • Solve. 2x − 5x − 3 = 0 2 ( 2x + 1) ( x − 3) = 0 2x + 1 = 0 or x−3= 0 −1 −1 +3 +3 2x = −1 or x=3 2 2 x = − 12
  24. 24. Page 2 - Finish it • Solve. 2x − 5x − 3 = 0 2 ( 2x + 1) ( x − 3) = 0 2x + 1 = 0 or x−3= 0 −1 −1 +3 +3 2x = −1 or x=3 2 2 x = − 12 ⎧ 1 ⎫ Answer: ⎨− , 3⎬ ⎩ 2 ⎭
  25. 25. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 0 2
  26. 26. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1
  27. 27. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 −11x − 6 + 10x = 0 2
  28. 28. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 2
  29. 29. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 2 ( 5x + 2 ) ( 2x − 3) = 0
  30. 30. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 2 ( 5x + 2 ) ( 2x − 3) = 0 5x + 2 = 0 or 2x − 3 = 0
  31. 31. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 2 ( 5x + 2 ) ( 2x − 3) = 0 5x + 2 = 0 or 2x − 3 = 0 −2 −2 +3 +3
  32. 32. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 2 ( 5x + 2 ) ( 2x − 3) = 0 5x + 2 = 0 or 2x − 3 = 0 −2 −2 +3 +3 5x = −2 or 2x = 3
  33. 33. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 2 ( 5x + 2 ) ( 2x − 3) = 0 5x + 2 = 0 or 2x − 3 = 0 −2 −2 +3 +3 5x = −2 or 2x = 3 5 5 2 2
  34. 34. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 2 ( 5x + 2 ) ( 2x − 3) = 0 5x + 2 = 0 or 2x − 3 = 0 −2 −2 +3 +3 5x = −2 or 2x = 3 5 5 2 2 x = −25 or x= 3 2
  35. 35. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 2 ( 5x + 2 ) ( 2x − 3) = 0 5x + 2 = 0 or 2x − 3 = 0 −2 −2 +3 +3 5x = −2 or 2x = 3 5 5 2 2 ⎧ 2 3⎫ Answer: ⎨− , ⎬ x = −25 or x= 3 2 ⎩ 5 2⎭
  36. 36. Page 3 - Your Turn • Solve. −16x = −4x 3
  37. 37. Page 3 - Your Turn • Solve. −16x = −4x 3 +4x 3 +4x 3
  38. 38. Page 3 - Your Turn • Solve. −16x = −4x 3 +4x 3 +4x 3 4x − 16x = 0 3
  39. 39. Page 3 - Your Turn • Solve. −16x = −4x 3 +4x 3 +4x 3 4x − 16x = 0 3 ( 4x x − 4 = 0 2 )
  40. 40. Page 3 - Your Turn • Solve. −16x = −4x 3 +4x 3 +4x 3 4x − 16x = 0 3 ( 4x x − 4 = 0 2 ) 4x ( x + 2 ) ( x − 2 ) = 0
  41. 41. Page 3 - Your Turn • Solve. −16x = −4x 3 +4x 3 +4x 3 4x − 16x = 0 3 ( 4x x − 4 = 0 2 ) 4x ( x + 2 ) ( x − 2 ) = 0 4x = 0 or x+2=0 or x−2=0
  42. 42. Page 3 - Your Turn • Solve. −16x = −4x 3 +4x 3 +4x 3 4x − 16x = 0 3 ( 4x x − 4 = 0 2 ) 4x ( x + 2 ) ( x − 2 ) = 0 4x = 0 or x+2=0 or x−2=0 4 4 −2 −2 +2 +2
  43. 43. Page 3 - Your Turn • Solve. −16x = −4x 3 +4x 3 +4x 3 4x − 16x = 0 3 ( 4x x − 4 = 0 2 ) 4x ( x + 2 ) ( x − 2 ) = 0 4x = 0 or x+2=0 or x−2=0 4 4 −2 −2 +2 +2 x=0 or x = −2 or x=2
  44. 44. Page 3 - Your Turn • Solve. −16x = −4x 3 +4x 3 +4x 3 4x − 16x = 0 3 ( 4x x − 4 = 0 2 ) 4x ( x + 2 ) ( x − 2 ) = 0 4x = 0 or x+2=0 or x−2=0 4 4 −2 −2 +2 +2 x=0 or x = −2 or x=2 Answer: {0, −2, 2}
  45. 45. Do you want to Play a GAME? • Check your knowledge on solving Quadratic Equations by playing Jeopardy. Ok, technically it’s called Challenge Board but it’s the same idea! • You have the option to play alone or against a friend or maybe a family member! • You could even arrange a time with a classmate to meet on Pronto to play. Try the App Share feature to see the same game board! • Finding the x-intercepts is the same as solving!
  46. 46. Fantastic Job! • You’ve finished reviewing Solving Quadratic Equations Part 2. • Exit and proceed to the Mastery Assignment.

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