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Solving quadratic equations part 2
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Solving quadratic equations part 2

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  • Transcript

    • 1. Solving Quadratic Equations PART 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. Page 1 - Finish it• Solve. 2 x − 3x − 18 = 0
    • 4. Page 1 - Finish it• Solve. 2 x − 3x − 18 = 0 ( x + 3) ( x − 6 ) = 0
    • 5. Page 1 - Finish it• Solve. 2 x − 3x − 18 = 0 ( x + 3) ( x − 6 ) = 0 x+3= 0 or x−6=0
    • 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. 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. 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. Page 1 - Your Turn 2• Solve. x + 7x = 170
    • 10. Page 1 - Your Turn 2• Solve. x + 7x = 170 −170 −170
    • 11. Page 1 - Your Turn 2• Solve. x + 7x = 170 −170 −170 2 x + 7x − 170 = 0
    • 12. Page 1 - Your Turn 2• Solve. x + 7x = 170 −170 −170 2 x + 7x − 170 = 0 ( x + 17 ) ( x − 10 ) = 0
    • 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. 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. 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. 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. Page 2 - Finish it• Solve. 2 2x − 5x − 3 = 0
    • 18. Page 2 - Finish it• Solve. 2 2x − 5x − 3 = 0 ( 2x + 1) ( x − 3) = 0
    • 19. Page 2 - Finish it• Solve. 2 2x − 5x − 3 = 0 ( 2x + 1) ( x − 3) = 0 2x + 1 = 0 or x−3= 0
    • 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. 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. 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. 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. 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. Page 2 - Your Turn• Solve. 2 11x + 6 − 10x = 0
    • 26. Page 2 - Your Turn• Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1
    • 27. Page 2 - Your Turn• Solve. 11x + 6 − 10x = 02 ( −1 11x + 6 − 10x 2 ) = 0 ⋅ −1 2 −11x − 6 + 10x = 0
    • 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. 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. 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. 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. 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. 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. 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. 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. Page 3 - Your Turn 3• Solve. −16x = −4x
    • 37. Page 3 - Your Turn 3• Solve. −16x = −4x +4x 3 +4x 3
    • 38. Page 3 - Your Turn 3• Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0
    • 39. Page 3 - Your Turn 3• Solve. −16x = −4x +4x 3 +4x 3 3 4x − 16x = 0 ( 2 4x x − 4 = 0)
    • 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. 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. 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. 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. 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. 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. Fantastic Job!• You’ve finished reviewing Solving Quadratic Equations Part 2.• Exit and proceed to the Homework Assignment.

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