Square Root Property and Completing the Square?

1: Solve for x using the Square Root Property:

x2 + 5 = 86

-9

9

-9, 9

2: x2 - 8 = 13

-√21, √21

-√21

-3, 7

3: For #3 - 6, what number can be added to both sides to produce a perfect square trinomial on the left? These questions offer practice in step 3 only, of the steps in 34.5.

.............................. x2 - 2x = 0

1

2

4

4: .............................. x2 + 2x = 0

-2

1

4

5: .............................. z2 - 14x = 0

-7

-49

49

6: .............................. x2 + 8x = 0

-16

16

64

7: Solve these equations by completing the square. Refer to the steps in assignment 34.5.

.............................. x2 - 8x + 12 = 0

3, 8

3, 4

2, 6

8: .............................. 4x2 + 9 = 12x

3/2

2, 3

2, 4

9: Distribute the 6 into the parentheses before beginning:

.............................. 6(p2 - 1) = 5p

-3/2, 2/3

-4, 7

-2/3, 3/2

10: Distribute the x into the parentheses before beginning:

.............................. x(6x - 5) = 6

-2/3, 3/2

4, 8

2, 3

11: .............................. x2 + 4x = 21

3, -7

-5, 5

-3, 8

12: .............................. x2 - 1/2 x - 3/16 = 0

-1/4, 3/4

-1/4, 2/3

-3/4, 1/4

13: .............................. m2 - 10m = 3

5 ± 2√7

-5 ± 2√7

3 ± √7

14: .............................. x2 + 2x = 35

-3, 5

-2, 7

-7, 5

15: .............................. r2 + 14r = -13

6, 7

-7, 1

-13, -1

16: .............................. 2x2 = 2x + 15

1 ± √29

2

1 ± √31

2

2 ± √22

2

17: .............................. x2 = 2x + 4

1 ± √5

2

1 ± √5

1 ± √6

18: .............................. 4t2 = 8t - 1

2 ±

√7

2

1 ±√3 2

1 ±

√3

2

19: Distribute the x into the parentheses before beginning:

.............................. x(x - 2) = 5

1 ± √6

1 ± √5

1 ±√6 2

20: .............................. 10x2 = 4x + 7

2 5 ± √74 5

2 5 ± √86 5

1 5 ± √74 10