PPT

1. by Teacher Ivy
SOLVING QUADRATIC
EQUATION BY
EXTRACTING SQUARE
ROOTS

2. FIND MY ROOTS
1.
2. -
3.
4. -
5.

3. FIND MY ROOTS
1. = ±4
2. = ±5
3. = ±7
4. = ±4
5. =± 11

5. FIND MY ROOTS
6.
7.
8.
9.
10.

6. FIND MY ROOTS
6. = =
7. = =
8. = =
9. = =3
10. ==

8. RECALL:SOLVE!

9. by Teacher Ivy
SOLVING QUADRATIC
EQUATION BY
EXTRACTING SQUARE
ROOTS

10. OBJECTIVES:
a.)Solve equations of the form
x2
= k and ax2
= k where k > 0.
b.)Solve equations of the form (ax
+ b)2
= k, where k > 0.

11. Objective a
●Solve equations of
the form x2
= k and ax2
= k where k > 0.

12. Example 1: x2
= 169
x = ± 13
The solutions are
13 and –13.
Solve for x by taking
the square root of
both sides. Use ± to
show both square
roots.
Substitute 13
and –13 into the
original equation.
x2
= 169
(–13)2
169
169 169
Check x2
= 169
(13)2
169
169 169 

13. Example 2.
m2
-121= 0
𝐦=± 𝟏𝟏
The solutions are 11 and –
11.
Solve for x by
taking the square
root of both sides.
Use ± to show
both square
roots.
Substitute 11
and –11 into the
original equation.
m2
= 121
(–11)2
= 121
121 = 121

Check m2
= 121
(11)2
= 121
121 = 121

𝒎=𝟏𝟐𝟏
𝒎=± √𝟏𝟐𝟏

14. Example 3. x2
- 37 =12

15. Example 3. 2x2
– 32 = 0
2x2
-32+32 = +32 Add 32 to both sides.
Divide both sides by 2.
Take the square root of both
sides. Use ± to show both
square roots.
2x2
= +32
x2
= 16
x = ±
x =± 4

16. Solve!
1.

17. 2.

18. 3.

19. 4.

20. 5.

21. 6.

22. 7.

23. Objective b:
• Solve equations of the
form k, where k > 0.

24. Example 1.
(x – 5)2
= 16 Take the square root of both
sides. Use ± to show both
square roots.
=
x – 5 = ±4
Write two equations, using both the
positive and negative square roots,
and solve each equation.
x – 5 = 4 or x – 5 = –4
x = 9 or x = 1
The solutions are 9 and 1.
x = 4+5 or x = –4+5

25. (3 𝑥− 3)2− 36=0

29. Solve!
1. 36
2. (x + 7)2
-81= 0
3. (2x -1)2
= 225
4. 5 75