Free Printable Solving Quadratic Equations using 3 Methods

1.

Write the question and show all work.
x²= 100

a)

10

b)

-10

c)

±10

d)

±50

2.

Write the question and show all work.4x²=100

a)

25

b)

±25

c)

5

d)

±5

3.

Write the question and show all work.
(x-5)² = 25

a)

±0

b)

±10

c)

10, 0

d)

-10, 0

4.

Write the question and show all work.
(x+3)²-5 = 9

a)

±√14 -3

b)

√14 - 3

c)

±11

d)

±5

5.

x² = 16

a)

± 4

b)

± 8

c)

4

d)

8

6.

3x² = 12

a)

± 2

b)

2

c)

± √12

d)

± 4

7.

-5x² = -50

a)

± 5

b)

± 10

c)

± √10

d)

-10

8.

x² + 4 = 68

a)

± 8

b)

± √8

c)

8

d)

± 64

9.

7x² + 1 = 8

a)

± 1

b)

± 7

c)

± √7

d)

± 8

10.

(x + 1) ² = 25

a)

± 5

b)

4 or -6

c)

-4 or 6

d)

± 4

11.

(x - 2) ² = 9

a)

± 3

b)

5 or -1

c)

-5 or 1

d)

± 9

12.

Solve by taking square roots:
k² - 6 = 43

a)

k = √37

b)

k = 37 or - 37

c)

k = 7, k = -7

d)

no solution

13.

Solve by taking square roots:
5b² - 4 = 41

a)

b = 9, b = -9

b)

b = 3, b = -3

c)

b = 8, b = -8

d)

no solution

14.

Solve using square roots.

a)

± 1/4

b)

± 9/36

c)

± 1/2

d)

No real solution

15.

Write the question and show all work.4x²=100

a)

25

b)

±25

c)

5

d)

±5

16.

Write the question and show all work.
(x-5)² = 25

a)

±0

b)

±10

c)

10, 0

d)

-10, 0

17.

Solve by taking square roots:
5m² + 1 = 6

a)

m = 0

b)

m = 1 or -1

c)

m = √7

d)

m = 7/5 m = -7/5

18.

Solve by taking square roots:
5b² - 4 = 41

a)

b = 9, b = -9

b)

b = 3, b = -3

c)

b = 8, b = -8

d)

no solutionb

19.

Solve by taking square roots:
3 + 9r² = 12

a)

r = 0

b)

no solution

c)

r = 3, r = -3

d)

r = 1, r = -1

20.

Solve using square roots.

a)

±72

b)

±12

c)

12

d)

No real solution

21.

Solve by taking square roots:
k² - 6 = 43

a)

k = √37

b)

k = 37 or - 37

c)

k = 7, k = -7

d)

no solution

22.

Solve
4m² - 100 = 0

a)

m=25, -25

b)

m=96

c)

m=5, -5

d)

m=-96

23.

Solve by taking square roots:
k² - 6 = 43

a)

k = √37

b)

k = 37 or - 37

c)

k = 7, k = -7

d)

no solution

24.

What are the solutions?

a)

0 and 8

b)

-2 and -4

c)

3 and -1

d)

2 and 4

25.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

26.

Solve for x x²- 4 = 76

a)

x = 4 , -4

b)

x = 4√5 , -4√5

c)

x = 80 , x = -80

d)

x = 5√4 or -5√4

27.

2x²= 30

a)

x= √5

b)

x= √30

c)

x= √15

d)

x= ±5

28.

a)

A

b)

B

c)

C

d)

D

29.

a)

A

b)

B

c)

C

d)

D

30.

a)

A

b)

B

c)

C

d)

D

31.

a)

A

b)

B

c)

C

d)

D

32.

a)

A

b)

B

c)

C

d)

D

33.

-5x² = -50

a)

± 5

b)

± 10

c)

± √10

d)

-10

34.

x² + 4 = 68

a)

± 8

b)

± √8

c)

8

d)

± 64

35.

Solve using square roots.

a)

± 1/4

b)

± 9/36

c)

± 1/2

d)

No real solution

36.

3x² - 1 = 14

a)

5

b)

-√5

c)

-√5, √5

d)

√5

37.

Simplify 4√75

a)

4√5

b)

12√5

c)

20√3

d)

7√3

38.

Simplify the following radical: 2√24

a)

4√6

b)

2√6

c)

24√2

d)

4√4

39.

5√80

a)

20√5

b)

4√5

c)

5√20

d)

4√5

40.

Simplify the following radical: √32

a)

3√2

b)

4√8

c)

16√2

d)

4√2

41.

√96

a)

4√6

b)

3√6

c)

6√5

d)

6√8

42.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

43.

To solve by completing the square, what needs to be moved in this equation?
x² = 9 - 4x

a)

the -4x

b)

the 9

c)

the x²

44.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

45.

When do you use the plus or minus symbol?
±

a)

After taking the square root of both sides

b)

After adding the square to both sides

c)

After taking half of b

d)

After setting the equation equal to zero

46.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

47.

Given the perfect square trinomial, identify the equivalent expression

x²-18x+81

a)

(x-18)²

b)

(x-9)²

c)

(x+81)²

d)

(x+9)²

48.

Solve the following quadratics equation by completing the square...

x² + 4x + 1 = 0

a)

x = -2 ± √3

b)

x = -3 ± √2

c)

x = 2 ± √3

d)

x = 2 ± √2

49.

Solve the following quadratics equation by completing the square...

x² + 12x + 8= 0

a)

x = -6 ± 2√7

b)

x = 6 ± 2√7

c)

x = 28 ± √6

d)

x = -28 ± √6

50.

What is one of the solutions to this equation?
(2x - 1)² = 49

a)

7

b)

-7

c)

-4

d)

-3

51.

Solve the equation by completing the square and then finding the roots.
x²+ 6x - 4 = 36

a)

x = -7, 7

b)

x = 4, -10

c)

x = -4 +- √7

d)

x = 10, -4

52.

Solve by method of your choice.

x² + 10x = -9

a)

1 and -12

b)

-1 and -9

c)

1 and -9

d)

1 and -1

53.

Solve. x² + 4x - 16 = 0

a)

b)

c)

d)

54.

What are the zeros?

a)

{2}

b)

{2,-4}

c)

No Solution

d)

{1,3}

55.

$v^2+2v-23=0$

a)

$\left\{9,1\right\}$

b)

$\left\{-2,-12\right\}$

c)

$\left\{-2+3\sqrt{3},-2-3\sqrt{3}\right\}$

d)

$\left\{-1+2\sqrt{6},\ -1-2\sqrt{6}\right\}$

56.

Solve by completing the square.
$x^2-4x-20=0$

a)

$x=\left\{-2\pm6\sqrt{2}\right\}$

b)

$x=\left\{2\pm6\sqrt{2}\right\}$

c)

$x=\left\{2\pm2\sqrt{6}\right\}$

d)

$x=\left\{-2\pm2\sqrt{6}\right\}$

57.

Solve.
$x^2-16x+48=0$

a)

$x=\left\{-12,\ 4\right\}$

b)

$x=\left\{-12,\ -4\right\}$

c)

$x=\left\{-4,\ 12\right\}$

d)

$x=\left\{4,\ 12\right\}$

58.

Solve the following quadratics equation by completing the square...

x² + 6x - 3 = 0

a)

$-3\pm2\sqrt{3}$

b)

$3\pm2\sqrt{3}$

c)

$12\pm\sqrt{3}$

d)

$-12\pm\sqrt{3}$

59.

Simplify the square root.

a)

A

b)

B

c)

C

d)

D

60.

Solve using square roots.
5b² - 4 = 41

a)

b = 9, b = -9

b)

b = 3, b = -3

c)

b = 8, b = -8

d)

no solution

61.

Solve
2x² - 3x - 2 = 0

a)

x = 1, x = -1

b)

x = -1/2, x = 2

c)

x = 1/2, x = 2

d)

x = 1/2, x = 1

62.

Solve for the values of x:
(x - 3)(x + 6) = 0

a)

{ -3, -6 }

b)

{ 3, -6 }

c)

{ -3, -6 }

d)

{ 3, 6 }

63.

Solve using Zero-Product Property.
(x+4)(x-3) = 0

a)

x = 4 and x = -3

b)

x = 2 and x = 1

c)

x = -4 and x = 3

d)

x = -2 and x = 1

64.

Solve
x² + 2x - 24 = 0

a)

x = -6, x = 4

b)

x = 6, x = -4

c)

x = 12, x = -2

d)

x = 8, x = -3

65.

Solve
x² + 9x + 20 = 0

a)

x = -2, x = -10

b)

x = -3, x = -4

c)

x = -4, x = -5

d)

x = -4, x = -6

66.

Solve
x² + 7x + 12 = 0

a)

x = -2, x = -10

b)

x = -3, x = -4

c)

x = -4, x = -5

d)

x = -4, x = -6

67.

Solve
x² + 13x + 12 = 0

a)

x = -1, x = -12

b)

x = -1, x = -24

c)

x = -2, x = -6

d)

x = -2, x = -12

68.

Solve by factoring: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

69.

Solve by factoring: x² + 3x - 18 = 0

a)

x = -3 and x = 6

b)

x = 3 and x = -6

c)

x = -9 and x = 2

d)

x = 9 and x = -2

70.

x² + 15x + 44 = 0

a)

{-8, 2}

b)

{-7, 5}

c)

{-11, -4}

d)

{-11}

71.

Solve by factoring: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

72.

Solve by factoring: x² + 3x - 18 = 0

a)

x = -3 and x = 6

b)

x = 3 and x = -6

c)

x = -9 and x = 2

d)

x = 9 and x = -2

73.

Solve for a by factoring.

a² + 2a - 24 = 0

a)

a = -6 and a = 4

b)

a = 6 and a = -4

c)

a = 12 and a = -2

d)

a = 8 and a = -3

74.

Solve by factoring:
x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

75.

Solve by factoring:
x² - 6x + 5 = 0

a)

-6, -1

b)

-5, -1

c)

1, 6

d)

5, 1

76.

Solve
x² + 13x + 12 = 0

a)

x = -12, -1

b)

x = 12, 1

c)

x = 13, 1

d)

x = -13, -1

77.

Solve by factoring.
z² - 6z - 27 = 0

a)

z = 3 or z = 9

b)

z = 3 or z = -9

c)

z = -3 or z = 9

d)

z = -3 or z = -9

78.

Solve by factoring.
z² - 18z + 81 = 0

a)

z = 9

b)

z = -9

c)

z = 9 or z = -9

79.

Solve:

k² - 2k - 24 = 0

a)

k = -4, 6

b)

k = -4, -6

c)

k = -6, 1

d)

k = 4, -6

80.

Solve using the Zero-Product Property.

(x + 4)(x − 3) = 0

a)

x = 4 and x = −3

b)

x = 2 and x = 1

c)

x = −4 and x = 3

d)

x = −2 and x = 1

81.

Solve using the Zero-Product Property.

7x(x − 6) = 0

a)

x =7 and x = −6

b)

x = 0 and x = 6

c)

x = 0 and x = −6

d)

x = 7 and x = 6

82.

Solve using the Zero-Product Property

(x −11)(5x + 1) = 0

a)

x = 11 or x = $-\frac{1}{5}$

b)

x = −11 or x = $-\frac{1}{5}$

c)

x = 11 or x = $\frac{1}{5}$

d)

x = −11 or x = $\frac{1}{5}$

83.

Factor and Solve: Remember the two numbers you choose when factoring, are not your solutions to the equation!

a² + 2a − 24 = 0

a)

a = −6, 4

b)

a = 6, −4

c)

a = 12, −2

d)

a = 8, −3

84.

Factor and Solve: Remember the two numbers you choose when factoring, are not your solutions to the equation!

x² + 13x + 12 = 0

a)

x = −12, −1

b)

x = 12, 1

c)

x = 13, 1

d)

x = −13, −1

85.

Factor and solve:

z² − 14z + 45 = 0

a)

z = 1, 45

b)

z = −1, 45

c)

z = −5, 9

d)

z = 5, 9

86.

x²+ 4x - 32 = 0

a)

x= -8, 4

b)

x= 8, -4

c)

x= -8, -4

d)

x = -2, 16

87.

Solve by taking the square root:

x² = 49

a)

-7

b)

7

c)

49

d)

±7

88.

2x²=100

a)

x = ±25

b)

x = ±√50

c)

x = ±√100

d)

x = ±√5

89.

Solve by taking square roots:
k² - 6 = 43

a)

k = √37

b)

k = 37 or - 37

c)

k = 7, k = -7

d)

no solution

90.

Solve by taking the square root:

4x² = 100

a)

±10

b)

±25

c)

±5

d)

5

Solving Quadratic Equations using 3 Methods

Total questions: 90

Worksheet time: 6hrs 48mins

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