This document provides instruction on solving quadratic equations. It begins with an introduction to quadratic equations and examples of their real-world applications. It then presents several examples of solving quadratic equations by factoring and setting each factor equal to 0. Various methods are demonstrated including solving by factoring trinomials and binomials. Finally, students are provided practice problems to solve quadratic equations on their own.

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
• Find a, b, and c. !3x ! x ! 5 = 0
2

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

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

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

10. 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

26. Page 5 - Try It & Your Turn
• Solve: 8x ! 26x ! 7 = 0
2
x ! 6x + 9 = 0
2
( 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: 8x ! 26x ! 7 = 0
2
x ! 6x + 9 = 0
2
( 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}

28. Page 5 - Try It & Your Turn
• Solve: 8x ! 26x ! 7 = 0
2
x ! 6x + 9 = 0
2
( 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}

29. Page 5 - Try It & Your Turn
• Solve: 8x ! 26x ! 7 = 0
2
x ! 6x + 9 = 0
2
( 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}

30. Page 5 - Try It & Your Turn
• Solve: 8x ! 26x ! 7 = 0
2
x ! 6x + 9 = 0
2
( 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}

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

32. Page 5 - Try It & Your Turn
• Solve: 8x ! 26x ! 7 = 0
2
x ! 6x + 9 = 0
2
( 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 x=
7
or x=!
1
2 4
Answer: {3} "7 1 %
Answer: # , ! &
$2 4 '

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

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

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

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

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

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

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

40. Page 6 - Your Turn
• Solve.
4a + 3a = 0
2
a ( 4a + 3) = 0
a=0 or 4a + 3 = 0
!3 !3
4a = !3
4 4
" 3% 3
Answer: #0, ! & a=!
$ 4' 4

41. Page 7 - Try It
• Solve.
x ! 25 = 0
2

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

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

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

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

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

47. Page 8 - Try It
• Solve.
5x ! 45x = 0
3

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

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

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

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

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

53. Page 8 - Try It
• Solve.
5x ! 45x = 0
3
(
5x x ! 9 = 0
2
)
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}

54. Page 9 - Your Turn
• Solve. 2y + 5y ! 3y = 0
3 2

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

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

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

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

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

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

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

62. Page 9 - Your Turn
• Solve. 2y + 5y ! 3y = 0
3 2
(
y 2y + 5y ! 3 = 0
2
)
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 '

63. 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.

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