1. Solving Quadratic
Equations
Module 10 - Topic 4
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. x − 3x − 18 = 0
2

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

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

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

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

11. Page 1 - Your Turn
• Solve. x + 7x = 170
2
−170 −170
x + 7x − 170 = 0
2

12. Page 1 - Your Turn
• Solve. x + 7x = 170
2
−170 −170
x + 7x − 170 = 0
2
( x + 17 ) ( x − 10 ) = 0

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

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

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

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. 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. 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. 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. 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. Page 2 - Your Turn
• Solve. 11x + 6 − 10x = 0
2

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
−11x − 6 + 10x = 0 2

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

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

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

39. Page 3 - Your Turn
• Solve. −16x = −4x 3
+4x 3 +4x 3
4x − 16x = 0
3
(
4x x − 4 = 0
2
)

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. 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. 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. 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. 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. 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 Mastery
Assignment.