Free Printable B2A2 11.1 Solving Quadratics

1.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

2.

Complete the square.
x² + 6x + ____

a)

x² + 6x + 9

b)

x² + 6x - 36

c)

x² + 6x + 36

d)

x² + 6x - 9

3.

Complete the Square
x² + 6x = 5

a)

(x + 3)² = 5

b)

(x + 6)² = 9

c)

(x + 3)² = 14

d)

(x + 6)² = 14

4.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

5.

Complete the square.
x² + 14x + ____

a)

x² + 14x - 196

b)

x² + 14x + 49

c)

x² + 14x - 49

d)

x² + 14x + 196

6.

Complete the Square
x² + 10x + ____

a)

x² + 10x - 100

b)

x² + 10x + 100

c)

x² + 10x - 25

d)

x² + 10x + 25

7.

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

a)

7

b)

-7

c)

-4

d)

-3

8.

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

9.

Solve the following equation by completing the square:
n² - 2n - 3 = 0

a)

{3 and-1}

b)

{4 and -4}

c)

{5 and -3}

d)

{8 and -7}

10.

Solve by completing the square.
y² + 10y = -9

a)

1 and -12

b)

-1 and -9

c)

1 and -9

d)

1 and -1

11.

Solve by completing the square.
x² +12x = 5

a)

X = 6 + √41 or 6 − √41

b)

X= 35 or 47

c)

X = −6 + √41 or −6 − √41

d)

X = √35 or √47

12.

Solve by completing the square:
k² − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

13.

a)

A

b)

B

c)

C

d)

D

14.

Solve
3x² + 5x - 12 = 0

a)

x = -4/3, x = 3

b)

x = 4/3, x = -3

c)

x = -1, x = 4

d)

x = 1, x = -4

15.

a)

36

b)

4

c)

6

d)

9

16.

a)

4

b)

16

c)

36

d)

64

17.

a)

4

b)

-4

c)

16

d)

-16

18.

a)

b)

c)

d)

19.

a)

2

b)

4

c)

8

d)

16

20.

a)

b)

c)

d)

21.

a)

$\frac{9}{2}$

b)

$\frac{3}{2}$

c)

$\left(\frac{3}{2}\right)^2$

d)

$\left(\frac{9}{2}\right)^2$

22.

Complete the square for the equation:

$x^2+6x-4=0$

a)

$\left(x+3\right)^2=4$

b)

$\left(x-3\right)^2=4$

c)

$\left(x+3\right)^2=13$

d)

$\left(x-3\right)^2=13$

23.

Complete the square for the equation:

$x^2-10x+7=0$

a)

$\left(x-5\right)^2=18$

b)

$\left(x+5\right)^2=18$

c)

$\left(x-5\right)^2=-7$

d)

$\left(x+5\right)^2=-7$

24.

Complete the square for the equation:

$x^2-24x+23=0$

a)

$\left(x+12\right)^2=121$

b)

$\left(x-12\right)^2=121$

c)

$\left(x+12\right)^2=144$

d)

$\left(x-12\right)^2=144$

25.

Solve by completing the square.
$x^2-8x-20=0$

a)

$x=\left\{-2,\ 10\right\}$

b)

$x=\left\{-10,\ 2\right\}$

c)

$x=\left\{-20,\ -8\right\}$

d)

$x=\left\{8,\ 20\right\}$

26.

Solve by completing the square.
$x^2-12x+20=0$

a)

$x=\left\{2,\ 10\right\}$

b)

$x=\left\{-10,\ -2\right\}$

c)

$x=\left\{-12,\ 20\right\}$

d)

$x=\left\{12,\ 20\right\}$

27.

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

a)

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

b)

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

c)

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

d)

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

28.

Solve by completing the square.
$x^2-6x-27=0$

a)

$x=\left\{-9,\ -3\right\}$

b)

$x=\left\{-3,\ 9\right\}$

c)

$x=\left\{-9,\ 3\right\}$

d)

$x=\left\{3,\ 9\right\}$

29.

Solve by completing the square.
$x^2-14x-15=0$

a)

$x=\left\{1,\ 15\right\}$

b)

$x=\left\{-15,\ -1\right\}$

c)

$x=\left\{-15,\ 1\right\}$

d)

$x=\left\{-1,\ 15\right\}$

30.

Solve by completing the square.
$x^2-6x-59=0$

a)

$x=\left\{\pm2\sqrt{17}+3\right\}$

b)

$x=\left\{\pm17\sqrt{2}+3\right\}$

c)

$x=\left\{\pm2\sqrt{17}-3\right\}$

d)

$x=\left\{\pm17\sqrt{2}-3\right\}$

31.

Solve by completing the square.
$x^2-4x-5=0$

a)

$x=\left\{-5,\ 1\right\}$

b)

$x=\left\{-1,\ 5\right\}$

c)

$x=\left\{-5,\ -1\right\}$

d)

$x=\left\{1,\ 5\right\}$

32.

Solve by completing the square.
$x^2-4x-21=0$

a)

$x=\left\{-7,\ 3\right\}$

b)

$x=\left\{3,\ 7\right\}$

c)

$x=\left\{-3,\ 7\right\}$

d)

$x=\left\{-7,\ -3\right\}$

33.

Solve by completing the square.
$x^2-16x+48=0$

a)

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

b)

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

c)

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

d)

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

34.

Solve by completing the square.
$x^2-8x-14=0$

a)

$x=\left\{\pm\sqrt{30}+4\right\}$

b)

$x=\left\{\pm\sqrt{4}+30\right\}$

c)

$x=\left\{\sqrt{30}+4\right\}$

d)

$x=\left\{\sqrt{30}-4\right\}$

35.

x² = 16

a)

± 4

b)

± 8

c)

4

d)

8

36.

3x² = 12

a)

± 2

b)

2

c)

± √12

d)

± 4

37.

-5x² = -50

a)

± 5

b)

± 10

c)

± √10

d)

-10

38.

x² + 4 = 68

a)

± 8

b)

± √8

c)

8

d)

± 64

39.

7x² + 1 = 8

a)

± 1

b)

± 7

c)

± √7

d)

± 8

40.

(x + 1) ² = 25

a)

± 5

b)

4 or -6

c)

-4 or 6

d)

± 4

41.

(x - 2) ² = 9

a)

± 3

b)

5 or -1

c)

-5 or 1

d)

± 9

42.

x² + 1 = 9

a)

± √8

b)

± 4

c)

± 8

d)

± 3

43.

(x - 2) ² = 49

a)

9 or -5

b)

± 9

c)

± 5

d)

± 7

44.

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

45.

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

a)

25

b)

±25

c)

5

d)

±5

46.

a)

A

b)

B

c)

C

d)

D

47.

16a² - 9 = 0

a)

a = ^-3/₄, ³/₄

b)

a = ^-4/₃, ⁴/₃

c)

a = ^-9/₁₆, ⁹/₁₆

d)

a = ^-16/₉, ¹⁶/₉

48.

5m² + 1 = 6

a)

m = 0

b)

m = 1 or -1

c)

m = √7

d)

m = 7/5 m = -7/5

49.

3 + 9r² = 12

a)

r = 0

b)

no solution

c)

r = 3, r = -3

d)

r = 1, r = -1

50.

4m² - 100 = 0

a)

m=25, -25

b)

m=96

c)

m=5, -5

d)

m=-96

51.

k² - 6 = 43

a)

k = √37

b)

k = 37 or - 37

c)

k = 7, k = -7

d)

no solution

52.

3x² - 1 = 14

a)

5

b)

-√5

c)

-√5, √5

d)

√5

53.

Solve.

x² +12 = 5

a)

x = ± 49

b)

No Real Solutions

c)

x = ± √7

d)

x = ± 3.5i

54.

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

55.

Solve the equation using Square Roots Method:

$x^2-100=0$

a)

x=10

b)

x=-10

c)

x= -10, 10

d)

x= -50,50

56.

Solve equation by using Square Roots Method:

$25x^2=4$

a)

$x=-\frac{5}{2},\ \frac{5}{2}$

b)

$x=\frac{2}{5}$

c)

$x=-\frac{2}{5},\ \frac{2}{5}$

d)

No Solution

57.

Solve by Using Square Roots Method:

$2x^2-3=-3$

a)

x= -2, 2

b)

$x=\sqrt[]{-3}$

c)

No Solution

d)

x= 0

58.

What are the solutions to $\left(x-6\right)^2=31$ using the square root method?

a)

A.

$x=6\pm\sqrt[]{31}$

b)

B.

$-6\pm\sqrt[]{31}$

c)

C.

$12\pm\sqrt[]{31}$

d)

D.

$x=-12\sqrt[]{31}$

59.

Solve the following quadratic equation: $4x^2-9=0$

a)

A. $x=\frac{3}{2}$ & $x=-\frac{3}{2}$

b)

B. $x=\frac{2}{3}$ & $x=\frac{-2}{3}$

c)

C. $x=\frac{9}{4}$

d)

D. $x=\frac{4}{9}$

60.

What are the solutions to $\left(x+5\right)^2-20=0$ using the square root method?

a)

$x=-5\pm\sqrt[]{20}$

b)

$x=5\pm\sqrt[]{20}$

c)

$x=5+\sqrt[]{20}$

d)

$x=-5-\sqrt[]{20}$

61.

Solve by using the Square Roots Method:

$\frac{1}{3}x^2+14=26$

a)

x=6

b)

x= -6, 6

c)

x= -4, 4

d)

x=-2, 2

62.

What are the solutions $\left(x+3\right)^2-13=0$ using the square root method?

a)

$x=-3\pm\sqrt[]{13}$

b)

$x=3\pm\sqrt[]{13}$

c)

$x=-3\pm\sqrt[]{-13}$

d)

$x=-3-\sqrt[]{13}$

63.

Solve the equation using the Square Roots Method:

$9x^2-1=63$

a)

$x=-\frac{64}{9},\ \frac{64}{9}$

b)

$x=-\frac{8}{3},\ \frac{8}{3}$

c)

$x=-\frac{3}{8},\ \frac{3}{8}$

d)

No Solution

64.

Solve the equation using Square Roots Method:

$\frac{1}{4}x^2-7=25$

a)

$x=-\sqrt[]{128},\ \sqrt[]{128}$

b)

$x=-\sqrt[]{8},\ \sqrt[]{8}$

c)

$x=-2\sqrt[]{2},\ 2\sqrt[]{2}$

d)

$x=-8\sqrt[]{2},\ 8\sqrt[]{2}$

65.

Simplify √40

a)

2√10

b)

4√10

c)

10√2

d)

10√4

66.

Simplify √125

a)

3√5

b)

5√5

c)

3√25

d)

5√3

67.

Simplify √192

a)

3√8

b)

8√3

c)

4√12

d)

2√24

68.

Simplify √300

a)

3√100

b)

3√10

c)

100√3

d)

10√3

69.

65

a)

Is a perfect square.

b)

Is not a perfect square.

70.

Which statement is NOT true?

a)

√169 = 13

b)

15² = 225

c)

4² = √16

d)

√324 = 18

71.

Simplify: $2\sqrt{48}$

a)

$8\sqrt{3}$

b)

$4\sqrt{12}$

c)

$9\sqrt{6}$

d)

$10\sqrt{2}$

72.

(a)

73.

(a)

74.

$\sqrt{512}=x\sqrt{2}$ What is the value of x? Hint: simplify the square root and see how your answer compares to what is written here.

(a)

B2A2 11.1 Solving Quadratics

Total questions: 74

Worksheet time: 3hrs 20mins

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