1. Solving Quadratic
Equations
Module 10 - Topic 4
PART 1

2. Why do we need to solve
Quadratic Equations?
• View this Discovery Education video to see a
use for Quadratic Equations AND why math is
cool!

3. Why do we need to solve
Quadratic Equations?
• View this Discovery Education video to see a
use for Quadratic Equations AND why math is
cool!
• Now, wasn’t that cool? I bet you never look at
a pumpkin the same way again!

4. Why do we need to solve
Quadratic Equations?
• View this Discovery Education video to see a
use for Quadratic Equations AND why math is
cool!
• Now, wasn’t that cool? I bet you never look at
a pumpkin the same way again!
• Let’s look at solving Quadratic Equations a
little closer.

5. What is a Quadratic Equation?
• View this Cool Math lesson introducing
Quadratic Equations.
• There are 2 pages of notes.
• Complete the Try It problems in your notebook
and check your answers on the next slide.

6. Page 2 - Try It
2
−3x − x − 5 = 0

7. Page 2 - Try It
2
• Find a, b, and c. −3x − x − 5 = 0

8. Page 2 - Try It
2
• Find a, b, and c. −3x − x − 5 = 0
a. -3
b. -1
c. -5

9. Page 2 - Try It
2
• Find a, b, and c. −3x − x − 5 = 0
a. -3
b. -1
c. -5
2
• Find a, b, and c. x −6=0

10. Page 2 - Try It
2
• Find a, b, and c. −3x − x − 5 = 0
a. -3
b. -1
c. -5
2
• Find a, b, and c. x −6=0
a. 1
b. 0 (The x term is missing so b is 0.)
c. -6

11. Solving Quadratic Equations by
Factoring
• View this Cool Math website to learn about
solving Quadratic Equations.
• There are 9 pages to view.
• Complete the Try It problems in your notebook
and check your answers on the next slides.

12. Page 4 - Try It
• Solve. 2
x + 8x + 12 = 0

13. Page 4 - Try It
• Solve. 2
x + 8x + 12 = 0
Factor the trinomial.

14. Page 4 - Try It
• Solve. 2
x + 8x + 12 = 0
Factor the trinomial.
( x + 6 )( x + 2 ) = 0

15. Page 4 - Try It
• Solve. 2
x + 8x + 12 = 0
Factor the trinomial.
( x + 6 )( x + 2 ) = 0
Split the factors
and set equal to 0.

16. Page 4 - Try It
• Solve. 2
x + 8x + 12 = 0
Factor the trinomial.
( x + 6 )( x + 2 ) = 0
Split the factors
and set equal to 0. x+6=0 or x+2=0

17. Page 4 - Try It
• Solve. 2
x + 8x + 12 = 0
Factor the trinomial.
( x + 6 )( x + 2 ) = 0
Split the factors
and set equal to 0. x+6=0 or x+2=0
Solve each
equation.

18. Page 4 - Try It
• Solve. 2
x + 8x + 12 = 0
Factor the trinomial.
( x + 6 )( x + 2 ) = 0
Split the factors
and set equal to 0. x+6=0 or x+2=0
Solve each −6 −6 −2 −2
equation.

19. Page 4 - Try It
• Solve. 2
x + 8x + 12 = 0
Factor the trinomial.
( x + 6 )( x + 2 ) = 0
Split the factors
and set equal to 0. x+6=0 or x+2=0
Solve each −6 −6 −2 −2
equation. x = −6 or x = −2

20. Page 4 - Try It
• Solve. 2
x + 8x + 12 = 0
Factor the trinomial.
( x + 6 )( x + 2 ) = 0
Split the factors
and set equal to 0. x+6=0 or x+2=0
Solve each −6 −6 −2 −2
equation. x = −6 or x = −2
Answer: {−6, −2}

21. Page 5 - Try It & Your Turn
• Solve:
2
x − 6x + 9 = 0

22. Page 5 - Try It & Your Turn
• Solve:
2
x − 6x + 9 = 0
( x − 3) ( x − 3) = 0

23. Page 5 - Try It & Your Turn
• Solve:
2
x − 6x + 9 = 0
( x − 3) ( x − 3) = 0
x−3= 0 or x − 3 = 0

24. Page 5 - Try It & Your Turn
• Solve:
2
x − 6x + 9 = 0
( x − 3) ( x − 3) = 0
x−3= 0 or x − 3 = 0
+3 +3 +3 +3

25. Page 5 - Try It & Your Turn
• Solve:
2
x − 6x + 9 = 0
( x − 3) ( x − 3) = 0
x−3= 0 or x − 3 = 0
+3 +3 +3 +3
x=3 or x=3

26. Page 5 - Try It & Your Turn
• Solve:
2
x − 6x + 9 = 0
( x − 3) ( x − 3) = 0
x−3= 0 or x − 3 = 0
+3 +3 +3 +3
x=3 or x=3
Answer: {3}

27. Page 5 - Try It & Your Turn
• Solve: 2
8x − 26x − 7 = 0
2
x − 6x + 9 = 0
( x − 3) ( x − 3) = 0
x−3= 0 or x − 3 = 0
+3 +3 +3 +3
x=3 or x=3
Answer: {3}

28. Page 5 - Try It & Your Turn
• Solve: 2
8x − 26x − 7 = 0
2
x − 6x + 9 = 0
( 2x − 7 ) ( 4x + 1) = 0
( x − 3) ( x − 3) = 0
x−3= 0 or x − 3 = 0
+3 +3 +3 +3
x=3 or x=3
Answer: {3}

29. Page 5 - Try It & Your Turn
• Solve: 2
8x − 26x − 7 = 0
2
x − 6x + 9 = 0
( 2x − 7 ) ( 4x + 1) = 0
( x − 3) ( x − 3) = 0
2x − 7 = 0 or 4x + 1 = 0
x−3= 0 or x − 3 = 0
+3 +3 +3 +3
x=3 or x=3
Answer: {3}

30. Page 5 - Try It & Your Turn
• Solve: 2
8x − 26x − 7 = 0
2
x − 6x + 9 = 0
( 2x − 7 ) ( 4x + 1) = 0
( x − 3) ( x − 3) = 0
2x − 7 = 0 or 4x + 1 = 0
x−3= 0 or x − 3 = 0 +7 +7 −1 −1
+3 +3 +3 +3
x=3 or x=3
Answer: {3}

31. Page 5 - Try It & Your Turn
• Solve: 2
8x − 26x − 7 = 0
2
x − 6x + 9 = 0
( 2x − 7 ) ( 4x + 1) = 0
( x − 3) ( x − 3) = 0
2x − 7 = 0 or 4x + 1 = 0
x−3= 0 or x − 3 = 0 +7 +7 −1 −1
+3 +3 +3 +3 2x = 7 or 4x = −1
x=3 or x=3
Answer: {3}

32. Page 5 - Try It & Your Turn
• Solve: 2
8x − 26x − 7 = 0
2
x − 6x + 9 = 0
( 2x − 7 ) ( 4x + 1) = 0
( x − 3) ( x − 3) = 0
2x − 7 = 0 or 4x + 1 = 0
x−3= 0 or x − 3 = 0 +7 +7 −1 −1
+3 +3 +3 +3 2x = 7 or 4x = −1
x=3 or x=3 7 1
x= or x=−
2 4
Answer: {3}

33. Page 5 - Try It & Your Turn
• Solve: 2
8x − 26x − 7 = 0
2
x − 6x + 9 = 0
( 2x − 7 ) ( 4x + 1) = 0
( x − 3) ( x − 3) = 0
2x − 7 = 0 or 4x + 1 = 0
x−3= 0 or x − 3 = 0 +7 +7 −1 −1
+3 +3 +3 +3 2x = 7 or 4x = −1
x=3 or x=3 7 1
x= or x=−
2 4
Answer: {3} 7 1 
Answer:  , − 
2 4 

34. Page 6 - Your Turn
• Solve. 2
4a + 3a = 0

35. Page 6 - Your Turn
• Solve. 2
4a + 3a = 0
a ( 4a + 3) = 0

36. Page 6 - Your Turn
• Solve. 2
4a + 3a = 0
a ( 4a + 3) = 0
a=0 or 4a + 3 = 0

37. Page 6 - Your Turn
• Solve. 2
4a + 3a = 0
a ( 4a + 3) = 0
a=0 or 4a + 3 = 0
−3 −3

38. Page 6 - Your Turn
• Solve. 2
4a + 3a = 0
a ( 4a + 3) = 0
a=0 or 4a + 3 = 0
−3 −3
4a = −3

39. Page 6 - Your Turn
• Solve. 2
4a + 3a = 0
a ( 4a + 3) = 0
a=0 or 4a + 3 = 0
−3 −3
4a = −3
4 4

40. Page 6 - Your Turn
• Solve. 2
4a + 3a = 0
a ( 4a + 3) = 0
a=0 or 4a + 3 = 0
−3 −3
4a = −3
4 4
3
a=−
4

41. Page 6 - Your Turn
• Solve. 2
4a + 3a = 0
a ( 4a + 3) = 0
a=0 or 4a + 3 = 0
−3 −3
4a = −3
4 4
 3 3
Answer: 0, −  a=−
 4 4

42. Page 7 - Try It
• Solve. 2
x − 25 = 0

43. Page 7 - Try It
• Solve. 2
x − 25 = 0
( x + 5 )( x − 5 ) = 0

44. Page 7 - Try It
• Solve. 2
x − 25 = 0
( x + 5 )( x − 5 ) = 0
x+5=0 or x−5=0

45. Page 7 - Try It
• Solve. 2
x − 25 = 0
( x + 5 )( x − 5 ) = 0
x+5=0 or x−5=0
−5 −5 +5 +5

46. Page 7 - Try It
• Solve. 2
x − 25 = 0
( x + 5 )( x − 5 ) = 0
x+5=0 or x−5=0
−5 −5 +5 +5
x = −5 or x=5

47. Page 7 - Try It
• Solve. 2
x − 25 = 0
( x + 5 )( x − 5 ) = 0
x+5=0 or x−5=0
−5 −5 +5 +5
x = −5 or x=5
Answer: {−5, 5}

48. Page 8 - Try It
• Solve. 3
5x − 45x = 0

49. Page 8 - Try It
• Solve. 3
5x − 45x = 0
( 2
)
5x x − 9 = 0

50. Page 8 - Try It
• Solve. 3
5x − 45x = 0
( 2
5x x − 9 = 0 )
5x ( x + 9 ) ( x − 9 ) = 0

51. Page 8 - Try It
• Solve. 3
5x − 45x = 0
( 2
5x x − 9 = 0 )
5x ( x + 9 ) ( x − 9 ) = 0
5x = 0 or x+9=0 or x−9=0

52. Page 8 - Try It
• Solve. 3
5x − 45x = 0
( 2
5x x − 9 = 0 )
5x ( x + 9 ) ( x − 9 ) = 0
5x = 0 or x+9=0 or x−9=0
5 5 −9 −9 +9 +9

53. Page 8 - Try It
• Solve. 3
5x − 45x = 0
( 2
5x x − 9 = 0 )
5x ( x + 9 ) ( x − 9 ) = 0
5x = 0 or x+9=0 or x−9=0
5 5 −9 −9 +9 +9
x=0 or x = −9 or x=9

54. Page 8 - Try It
• Solve. 3
5x − 45x = 0
( 2
5x x − 9 = 0 )
5x ( x + 9 ) ( x − 9 ) = 0
5x = 0 or x+9=0 or x−9=0
5 5 −9 −9 +9 +9
x=0 or x = −9 or x=9
Answer: {0, −9, 9}

55. Page 9 - Your Turn
3 2
• Solve. 2y + 5y − 3y = 0

56. Page 9 - Your Turn
3 2
• Solve. 2y + 5y − 3y = 0
( 2
y 2y + 5y − 3 = 0)

57. Page 9 - Your Turn
3 2
• Solve. 2y + 5y − 3y = 0
( 2
y 2y + 5y − 3 = 0 )
y ( 2y − 1) ( y + 3) = 0

58. Page 9 - Your Turn
3 2
• Solve. 2y + 5y − 3y = 0
( 2
y 2y + 5y − 3 = 0 )
y ( 2y − 1) ( y + 3) = 0
y=0 or 2y − 1 = 0 or y+3= 0

59. Page 9 - Your Turn
3 2
• Solve. 2y + 5y − 3y = 0
( 2
y 2y + 5y − 3 = 0 )
y ( 2y − 1) ( y + 3) = 0
y=0 or 2y − 1 = 0 or y+3= 0
+1 +1 −3 −3

60. Page 9 - Your Turn
3 2
• Solve. 2y + 5y − 3y = 0
( 2
y 2y + 5y − 3 = 0 )
y ( 2y − 1) ( y + 3) = 0
y=0 or 2y − 1 = 0 or y+3= 0
+1 +1 −3 −3
2y = 1 or y = −3

61. Page 9 - Your Turn
3 2
• Solve. 2y + 5y − 3y = 0
( 2
y 2y + 5y − 3 = 0 )
y ( 2y − 1) ( y + 3) = 0
y=0 or 2y − 1 = 0 or y+3= 0
+1 +1 −3 −3
2y = 1 or y = −3
2 2

62. Page 9 - Your Turn
3 2
• Solve. 2y + 5y − 3y = 0
( 2
y 2y + 5y − 3 = 0 )
y ( 2y − 1) ( y + 3) = 0
y=0 or 2y − 1 = 0 or y+3= 0
+1 +1 −3 −3
2y = 1 or y = −3
2 2
y= 1
2

63. Page 9 - Your Turn
3 2
• Solve. 2y + 5y − 3y = 0
( 2
y 2y + 5y − 3 = 0 )
y ( 2y − 1) ( y + 3) = 0
y=0 or 2y − 1 = 0 or y+3= 0
+1 +1 −3 −3
2y = 1 or y = −3
2 2
 1  y= 1
2
Answer: 0, , −3
 2 

64. Algebra Cruncher
• Practice solving more Quadratic Equations at this Cool
Math website.
• Select the “Give me a Problem” button to try new
problems.
• Do your work in a notebook before entering your answer.
• When you select “What’s the Answer?” your answer is
erased and correct answer is displayed. Having your
work in a notebook will allow you to compare your
answer to the correct answer.
• Keep working problems until you get 3 in a row correct.

65. Fantastic Job!
• You’ve finished reviewing Solving Quadratic
Equations Part 1.
• Exit and proceed to Part 2.