Quadratic Equations By Completing the Square

Kuta Software - Infinite Algebra 2

Name___________________________________

Solving Quadratic Equations By Completing the SquareDate________________

Period____

Solve each equation by completing the square.

1) p 2 + 14 p ? 38 = 0

2) v 2 + 6v ? 59 = 0

3) a 2 + 14a ? 51 = 0

4) x 2 ? 12 x + 11 = 0

5) x 2 + 6 x + 8 = 0

6) n 2 ? 2n ? 3 = 0

7) x 2 + 14 x ? 15 = 0

8) k 2 ? 12k + 23 = 0

9) r 2 ? 4r ? 91 = 7

10) x 2 ? 10 x + 26 = 8

11) k 2 ? 4k + 1 = ?5

12) b 2 + 2b = ?20

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Worksheet by Kuta Software LLC

13) v 2 ? 6v = ?91

14) n 2 = 18n + 40

15) 5k 2 = 60 ? 20k

16) 6 x 2 ? 48 = ?12 x

17) 8 x 2 + 16 x = 42

18) 9n 2 + 79 = ?18n

19) 2a 2 = ?6 + 8a

20) 2 x 2 ? 5 x + 67 = 0

21) 4n 2 + 4n + 36 = 0

22) 7k 2 ? 16k + 100 = 0

23) 10 p 2 + 4 p + 77 = 9

24) 3 x 2 = ?4 + 8 x

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Algebra 2

Name___________________________________

Solving Quadratic Equations By Completing the SquareDate________________

Period____

Solve each equation by completing the square.

1) p 2 + 14 p ? 38 = 0

{?7 +

2) v 2 + 6v ? 59 = 0

87 }

87, ?7 ?

3) a 2 + 14a ? 51 = 0

{?3 + 2

17, ?3 ? 2 17 }

4) x 2 ? 12 x + 11 = 0

{3, ?17}

{11, 1}

5) x 2 + 6 x + 8 = 0

6) n 2 ? 2n ? 3 = 0

{?2, ?4}

{3, ?1}

7) x 2 + 14 x ? 15 = 0

8) k 2 ? 12k + 23 = 0

{6 +

{1, ?15}

9) r 2 ? 4r ? 91 = 7

{2 +

102, 2 ?

10) x 2 ? 10 x + 26 = 8

102 }

11) k 2 ? 4k + 1 = ?5

{2 + i

13 }

13, 6 ?

{5 +

7}

12) b 2 + 2b = ?20

2, 2 ? i 2 }

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7, 5 ?

{?1 + i

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19, ?1 ? i 19 }

Worksheet by Kuta Software LLC

13) v 2 ? 6v = ?91

{3 + i

14) n 2 = 18n + 40

82, 3 ? i 82 }

{20, ?2}

15) 5k 2 = 60 ? 20k

16) 6 x 2 ? 48 = ?12 x

{2, ?6}

{2, ?4}

17) 8 x 2 + 16 x = 42

18) 9n 2 + 79 = ?18n

{

{ }

3 7

,?

2 2

19) 2a 2 = ?6 + 8a

{

21) 4n 2 + 4n + 36 = 0

?1 + i 35 ?1 ? i 35

,

2

2

?1 + 13i ?1 ? 13i

,

5

5

5 + i 511 5 ? i 511

,

4

4

}

22) 7k 2 ? 16k + 100 = 0

}

23) 10 p 2 + 4 p + 77 = 9

{

}

20) 2 x 2 ? 5 x + 67 = 0

{3, 1}

{

?3 + i 70 ?3 ? i 70

,

3

3

{

8 + 2i 159 8 ? 2i 159

,

7

7

}

24) 3 x 2 = ?4 + 8 x

}

{ }

2,

2

3

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Worksheet by Kuta Software LLC

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