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.        2
               x − 3x − 18 = 0
Page 1 - Finish it
• Solve.         2
               x − 3x − 18 = 0

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

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

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

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

               ( x + 3) ( x − 6 ) = 0
            x...
Page 1 - Your Turn
              2
• Solve.     x + 7x = 170
Page 1 - Your Turn
              2
• Solve.     x + 7x = 170
              −170   −170
Page 1 - Your Turn
                 2
• Solve.     x + 7x = 170
                 −170   −170
             2
            x ...
Page 1 - Your Turn
                   2
• Solve.        x + 7x = 170
                   −170       −170
               2
 ...
Page 1 - Your Turn
                   2
• Solve.        x + 7x = 170
                   −170       −170
               2
 ...
Page 1 - Your Turn
                   2
• Solve.        x + 7x = 170
                   −170       −170
               2
 ...
Page 1 - Your Turn
                   2
• Solve.        x + 7x = 170
                   −170       −170
               2
 ...
Page 1 - Your Turn
                   2
• Solve.        x + 7x = 170
                   −170       −170
               2
 ...
Page 2 - Finish it
• Solve.     2
           2x − 5x − 3 = 0
Page 2 - Finish it
• Solve.        2
             2x − 5x − 3 = 0

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

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

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

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

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

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

           ( 2x + 1) ( x − 3) = 0
      2x + 1 = 0  ...
Page 2 - Your Turn
• Solve.                2
            11x + 6 − 10x = 0
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
                         3
• Solve.    −16x = −4x
Page 3 - Your Turn
                            3
• Solve.      −16x = −4x
           +4x 3    +4x 3
Page 3 - Your Turn
                             3
• Solve.      −16x = −4x
           +4x 3     +4x 3
              3
    ...
Page 3 - Your Turn
                                   3
• Solve.      −16x = −4x
           +4x 3           +4x 3
        ...
Page 3 - Your Turn
                                    3
• Solve.       −16x = −4x
            +4x 3           +4x 3
     ...
Page 3 - Your Turn
                                    3
• Solve.       −16x = −4x
            +4x 3           +4x 3
     ...
Page 3 - Your Turn
                                     3
• Solve.       −16x = −4x
            +4x 3            +4x 3
   ...
Page 3 - Your Turn
                                     3
• Solve.       −16x = −4x
            +4x 3            +4x 3
   ...
Page 3 - Your Turn
                                     3
• Solve.       −16x = −4x
            +4x 3            +4x 3
   ...
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...
Upcoming SlideShare
Loading in...5
×

Module 10 Topic 4 solving quadratic equations part 2

5,344

Published on

Published in: Education, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
5,344
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
0
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide









































  • Module 10 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. 2 x − 3x − 18 = 0
    4. 4. Page 1 - Finish it • Solve. 2 x − 3x − 18 = 0 ( x + 3) ( x − 6 ) = 0
    5. 5. Page 1 - Finish it • Solve. 2 x − 3x − 18 = 0 ( x + 3) ( x − 6 ) = 0 x+3= 0 or x−6=0
    6. 6. Page 1 - Finish it • Solve. 2 x − 3x − 18 = 0 ( x + 3) ( x − 6 ) = 0 x+3= 0 or x−6=0 −3 −3 +6 +6
    7. 7. Page 1 - Finish it • Solve. 2 x − 3x − 18 = 0 ( 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. 2 x − 3x − 18 = 0 ( 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 2 • Solve. x + 7x = 170
    10. 10. Page 1 - Your Turn 2 • Solve. x + 7x = 170 −170 −170
    11. 11. Page 1 - Your Turn 2 • Solve. x + 7x = 170 −170 −170 2 x + 7x − 170 = 0
    12. 12. Page 1 - Your Turn 2 • Solve. x + 7x = 170 −170 −170 2 x + 7x − 170 = 0 ( x + 17 ) ( x − 10 ) = 0
    13. 13. Page 1 - Your Turn 2 • Solve. x + 7x = 170 −170 −170 2 x + 7x − 170 = 0 ( x + 17 ) ( x − 10 ) = 0 x + 17 = 0 or x − 10 = 0
    14. 14. Page 1 - Your Turn 2 • Solve. x + 7x = 170 −170 −170 2 x + 7x − 170 = 0 ( x + 17 ) ( x − 10 ) = 0 x + 17 = 0 or x − 10 = 0 −17 −17 +10 +10
    15. 15. Page 1 - Your Turn 2 • Solve. x + 7x = 170 −170 −170 2 x + 7x − 170 = 0 ( 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 2 • Solve. x + 7x = 170 −170 −170 2 x + 7x − 170 = 0 ( 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. 2 2x − 5x − 3 = 0
    18. 18. Page 2 - Finish it • Solve. 2 2x − 5x − 3 = 0 ( 2x + 1) ( x − 3) = 0
    19. 19. Page 2 - Finish it • Solve. 2 2x − 5x − 3 = 0 ( 2x + 1) ( x − 3) = 0 2x + 1 = 0 or x−3= 0
    20. 20. Page 2 - Finish it • Solve. 2 2x − 5x − 3 = 0 ( 2x + 1) ( x − 3) = 0 2x + 1 = 0 or x−3= 0 −1 −1 +3 +3
    21. 21. Page 2 - Finish it • Solve. 2 2x − 5x − 3 = 0 ( 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. 2 2x − 5x − 3 = 0 ( 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. 2 2x − 5x − 3 = 0 ( 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. 2 2x − 5x − 3 = 0 ( 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. 2 11x + 6 − 10x = 0
    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 2 −11x − 6 + 10x = 0
    28. 28. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 2 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0
    29. 29. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 2 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 ( 5x + 2 ) ( 2x − 3) = 0
    30. 30. Page 2 - Your Turn • Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 2 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 ( 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 2 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 ( 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 2 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 ( 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 2 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 ( 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 2 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 ( 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 2 −11x − 6 + 10x = 0 2 10x − 11x − 6 = 0 ( 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 3 • Solve. −16x = −4x
    37. 37. Page 3 - Your Turn 3 • Solve. −16x = −4x +4x 3 +4x 3
    38. 38. Page 3 - Your Turn 3 • Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0
    39. 39. Page 3 - Your Turn 3 • Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0 ( 2 4x x − 4 = 0)
    40. 40. Page 3 - Your Turn 3 • Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0 ( 2 4x x − 4 = 0 ) 4x ( x + 2 ) ( x − 2 ) = 0
    41. 41. Page 3 - Your Turn 3 • Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0 ( 2 4x x − 4 = 0 ) 4x ( x + 2 ) ( x − 2 ) = 0 4x = 0 or x+2=0 or x−2=0
    42. 42. Page 3 - Your Turn 3 • Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0 ( 2 4x x − 4 = 0) 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 3 • Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0 ( 2 4x x − 4 = 0) 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 3 • Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0 ( 2 4x x − 4 = 0) 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.

    ×