©Y ZKkuXtRad ESCoYfFt3wLaBrueT ALVLXC1.5 3 sAwlPlZ yreiegth1t3sS Nr9eOsCe4rHvJe0dF.1 J PMnacdleD awfirtrhC 2Ikncfkizndigtieb aABlpg7embirCat G2b.G Worksheet by Kuta Software LLC
Grade 10 Academic MathID: 1
Name___________________________________
Date________________Solving Quadratics by Completing the Square
Solve each equation by completing the square. (every 6 questions is another level of difficulty)
1)
n
2 + 10
n
− 24 = 0 2)
v
2 − 8
v
+ 12 = 0
3)
m
2 − 10
m
− 24 = 0 4)
m
2 + 12
m
+ 27 = 0
5)
x
2 + 6
x
− 30 = 0 6)
b
2 + 16
b
+ 50 = 0
7)
3
v
2 − 12
v
− 63 = 0 8)
5
r
2 + 10
r
− 15 = 0
9)
k
2 + 10
k
− 24 = 0 10)
7
k
2 + 14
k
− 56 = 0
11)
r
2 + 16
r
− 80 = 0 12)
x
2 − 6
x
− 78 = 0
13)
x
2 − 26
x
+ 18 = −7
x
14)
10
m
2 + 11
m
− 20 =
−4 + 5
m
15)
x
2 + 10
x
− 66 =
10 − 5
x
16)
3
v
2 + 24
v
− 96 =
−5
v
2 + 1
17)
5
x
2 + 21
x
− 91 = −9 18)
4
v
2 + 13 =
−1 + 3
v
2 − 9
v
©u PK2u7tDax sSpowftt2wWa0rHev 9LYLHCn.S E wAslrl3 2rsikg8hKtwsI 8rGeTsyeorUvueZdl.o 2 8MvaQdseC 2wDixtrhI EIwnZfuipnriFtnev 0APlmgJejbWr7a6 P2a.G Worksheet by Kuta Software LLC
Grade 10 Academic MathID: 1
Name___________________________________
Date________________Solving Quadratics by Completing the Square
Solve each equation by completing the square. (every 6 questions is another level of difficulty)
1)
n
2 + 10
n
− 24 = 0
{2, −12}2)
v
2 − 8
v
+ 12 = 0
{6, 2}
3)
m
2 − 10
m
− 24 = 0
{12, −2}4)
m
2 + 12
m
+ 27 = 0
{−3, −9}
5)
x
2 + 6
x
− 30 = 0
{
−3 + 39,
−3 −
39}6)
b
2 + 16
b
+ 50 = 0
{
−8 + 14,
−8 −
14}7)
3
v
2 − 12
v
− 63 = 0
{7, −3}8)
5
r
2 + 10
r
− 15 = 0
{1, −3}
9)
k
2 + 10
k
− 24 = 0
{2, −12}10)
7
k
2 + 14
k
− 56 = 0
{2, −4}
11)
r
2 + 16
r
− 80 = 0
{4, −20}12)
x
2 − 6
x
− 78 = 0
{
3 + 87,
3 −
87}
13)
x
2 − 26
x
+ 18 = −7
x
{18, 1}14)
10
m
2 + 11
m
− 20 =
−4 + 5
m
{1,
− 85}
15)
x
2 + 10
x
− 66 =
10 − 5
x
{4, −19}16)
3
v
2 + 24
v
− 96 =
−5
v
2 + 1
{
−6 + 2304
,
−6 −
2304 }
17)
5
x
2 + 21
x
− 91 = −9
{
−21 + 208110
,
−21 −
208110 }
18)
4
v
2 + 13 =
−1 + 3
v
2 − 9
v
{−2, −7}
©5 XKBuQtDal WS6ojfYtLwfa9rYex 3LfLaCp.Z A IAyl4lX mrsiXgPhxt5sr zrnegsuebr9vseIdc.r 9 oM5ajdpem Cwvi6t5hB HIKn9fiiln2iTtde8 yAwlcgVeWbkrQa8 B2z.u Worksheet by Kuta Software LLC
Grade 10 Academic MathID: 2
Name___________________________________
Date________________Solving Quadratics by Completing the Square
Solve each equation by completing the square. (every 6 questions is another level of difficulty)
1)
x
2 − 14
x
− 11 = 0 2)
x
2 − 14
x
+ 13 = 0
3)
k
2 − 10
k
+ 9 = 0 4)
b
2 − 8
b
− 22 = 0
5)
x
2 + 4
x
− 32 = 0 6)
n
2 + 2
n
− 63 = 0
7)
4
a
2 − 8
a
− 32 = 0 8)
5
n
2 + 10
n
− 15 = 0
9)
4
x
2 + 16
x
− 9 = 0 10)
p
2 − 6
p
− 49 = 0
11)
5
n
2 + 20
n
− 60 = 0 12)
n
2 + 14
n
− 71 = 0
13)
9
m
2 + 15
m
− 3 = 8
m
2 14)
a
2 − 12 =
−8 + 3
a
15)
9
x
2 − 10
x
− 82 =
−5 − 12
x
16)
−9
n
2 + 30 =
−10
n
2 − 11
n
17)
k
2 + 12
k
− 6 = 7
k
18)
r
2 − 71 =
r
©b mKWuXtUay 4SloyfDtgwwaRrCe0 SLKL1CO.P i NAclwlt ErwiCgzhatas9 TrzeysVeirkvceudn.Y K SMfaEdLeq bwmi6tHhG zIpn3fKimnNiAtiej MA3lZguejbPrGak Y2s.k Worksheet by Kuta Software LLC
Grade 10 Academic MathID: 2
Name___________________________________
Date________________Solving Quadratics by Completing the Square
Solve each equation by completing the square. (every 6 questions is another level of difficulty)
1)
x
2 − 14
x
− 11 = 0
{
7 +
2 15,
7 −
2 15}2)
x
2 − 14
x
+ 13 = 0
{13, 1}
3)
k
2 − 10
k
+ 9 = 0
{9, 1}4)
b
2 − 8
b
− 22 = 0
{
4 + 38,
4 −
38}5)
x
2 + 4
x
− 32 = 0
{4, −8}6)
n
2 + 2
n
− 63 = 0
{7, −9}
7)
4
a
2 − 8
a
− 32 = 0
{4, −2}8)
5
n
2 + 10
n
− 15 = 0
{1, −3}
9)
4
x
2 + 16
x
− 9 = 0
{
12
,
− 92}
10)
p
2 − 6
p
− 49 = 0
{
3 + 58,
3 −
58}
11)
5
n
2 + 20
n
− 60 = 0
{2, −6}12)
n
2 + 14
n
− 71 = 0
{
−7 +
2 30,
−7 −
2 30}
13)
9
m
2 + 15
m
− 3 = 8
m
2
{
−15 + 2372
,
−15 −
2372 }
14)
a
2 − 12 =
−8 + 3
a
{4, −1}
15)
9
x
2 − 10
x
− 82 =
−5 − 12
x
{
−1 + 6949
,
−1 −
6949 }
16)
−9
n
2 + 30 =
−10
n
2 − 11
n
{−5, −6}
17)
k
2 + 12
k
− 6 = 7
k
{1, −6}18)
r
2 − 71 =
r
{
1 + 2852
,
1 −
2852 }
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Grade 10 Academic MathID: 3
Name___________________________________
Date________________Solving Quadratics by Completing the Square
Solve each equation by completing the square. (every 6 questions is another level of difficulty)
1)
n
2 − 8
n
+ 15 = 0 2)
k
2 − 12
k
+ 20 = 0
3)
k
2 + 8
k
+ 8 = 0 4)
n
2 + 14
n
+ 42 = 0
5)
r
2 + 2
r
− 28 = 0 6)
m
2 + 10
m
+ 16 = 0
7)
7
v
2 + 14
v
− 11 = 0 8)
3
x
2 + 18
x
− 87 = 0
9)
3
n
2 + 6
n
− 45 = 0 10)
x
2 − 14
x
+ 1 = 0
11)
a
2 − 2
a
− 35 = 0 12)
x
2 − 18
x
+ 17 = 0
13)
7
a
2 − 19
a
=
−12
a
+ 14 14)
n
2 + 7
n
− 38 = 7
15)
−9
a
2 + 6
a
− 129 =
−9
a
− 10
a
2 16)
5
x
2 + 17
x
− 44 = −7
x
2
17)
4
v
2 +
v
− 22 =
v
2 18)
v
2 + 7
v
− 129 = −8
©v rKWubtIan pSBo4fTtpwTa2reeV QLfLfCY.T f WAjlDlB Br4iFgEh1tpsQ JruersMeZrvvyebdO.P 3 NMYaQdoeo cwBirtZht TIRnOf3iRniiMt6er KAqlAgxeYbIr8aO e2w.V Worksheet by Kuta Software LLC
Grade 10 Academic MathID: 3
Name___________________________________
Date________________Solving Quadratics by Completing the Square
Solve each equation by completing the square. (every 6 questions is another level of difficulty)
1)
n
2 − 8
n
+ 15 = 0
{5, 3}2)
k
2 − 12
k
+ 20 = 0
{10, 2}
3)
k
2 + 8
k
+ 8 = 0
{
−4 +
2 2,
−4 −
2 2}4)
n
2 + 14
n
+ 42 = 0
{
−7 + 7,
−7 −
7}5)
r
2 + 2
r
− 28 = 0
{
−1 + 29,
−1 −
29}6)
m
2 + 10
m
+ 16 = 0
{−2, −8}
7)
7
v
2 + 14
v
− 11 = 0
{
−7 +
3 147
,
−7 −
3 147 }
8)
3
x
2 + 18
x
− 87 = 0
{
−3 + 38,
−3 −
38}
9)
3
n
2 + 6
n
− 45 = 0
{3, −5}10)
x
2 − 14
x
+ 1 = 0
{
7 +
4 3,
7 −
4 3}
11)
a
2 − 2
a
− 35 = 0
{7, −5}12)
x
2 − 18
x
+ 17 = 0
{17, 1}
13)
7
a
2 − 19
a
=
−12
a
+ 14
{2, −1}14)
n
2 + 7
n
− 38 = 7
{
−7 + 2292
,
−7 −
2292 }
15)
−9
a
2 + 6
a
− 129 =
−9
a
− 10
a
2
{
−15 + 7412
,
−15 −
7412 }
16)
5
x
2 + 17
x
− 44 = −7
x
2
{
43
,
− 114 }
17)
4
v
2 +
v
− 22 =
v
2
{
−1 + 2656
,
−1 −
2656 }
18)
v
2 + 7
v
− 129 = −8
{
−7 + 5332
,
−7 −
5332 }