Download 1. Solve the equation by using the property of square root: a. x2 = 1

1. Solve the equation by using the property of square root:
a. x2 = 1
Ans: x = ±1
b. x2 = 4
Ans: x = ±2
c. x2 = 16
Ans: x = ±4
d. x2 = 49
Ans: x = ±7
e. x2 = 7
√
Ans: x = ± 7
f. x2 = 21
√
Ans: x = ± 21
g. x2 = 39
√
Ans: x = ± 39
h. x2 = 98
√
Ans: x = ±7 2
i. x2 = 50
√
Ans: x = ±5 2
j. x2 = 200
√
Ans: x = ±10 2
k. x2 = 18
√
Ans: x = ±3 2
l. x2 = 72
√
Ans: x = ±6 2
m. x2 = 27
√
Ans: x = ±3 3
n. x2 = −2
Ans: No (real number) solution.
o. x2 = −5
Ans: No (real number) solution.
p. x2 = 0
Ans: x = 0
2
q. (x − 4) = 12
√
Ans: x = 4 ± 2 3
2
l. (x + 13) = 31
√
Ans: x = −13 ± 31
2
m. (x − 24) = −17
Ans: No (real number) solution.
2
n. (2x − 5) = 6
√
5± 6
Ans: x =
2
2
o. (3x + 7) = 3
√
−7 ± 3
Ans: x =
3
2
p. (6x + 10) = 5
√
−10 ± 5
Ans: x =
6
x
2
1
q.
+3 =
3
2
√
√
3 2
−18 ± 3 2
Ans: x = −9 ±
=
2
2
2
r. (2x − 5) = 0
5
2
2. Solve the equation by Factoring:
Ans: x =
a. 3x2 + x = 0
1
Ans: 0, −
3
b. x2 + 3x − 10 = 0
Ans: {2, −5}
c. 2x2 − 3x = 20
5
Ans: 4, −
2
d. x2 + 5x + 6 = 20
Ans: {−7, 2}
e. x2 + 10x + 9 = 33
Ans: {−12, 2}
f. 2x2 + 5x = 0
5
Ans: 0, −
2
g. x2 − 4x − 5 = 0
Ans: {−1, 5}
h. x2 + 6x = −9
Ans: {−3}
i. x2 − 8x + 12 = 0
Ans: {6, 2}
j. x2 + 6x + 8 = 35
Ans: {−9, 3}
k. (x + 1)(x − 2) = 70
Ans: {−8, 9}
l. 2x2 + 5x − 7 = 0
7
Ans: 1, −
2
m. 4x2 + 5x − 6 = 0
Ans:
−2,
3
4
n. x2 − 4x − 5 = 0
Ans: {−1, 5}
o. x2 + 6x = −9
Ans: {−3}
p. (x + 1)(x − 2) = 70
Ans: {−8, 9}
q. 4x2 + 5x − 6 = 0
3
Ans: −2,
4
r. 4x2 − 5x + 1 = 0
1
Ans: 1,
4
s. x2 = 100
Ans: {−10, 10}
t. 4x2 − 5x + 1 = 0
1
Ans: 1,
4
u. x2 + 3x − 4 = 0
Ans: {1, −4}
v. x2 + 4x + 4 = 0
Ans: {−2}
3. Solve the equation by completing the square:
a. x2 + 10x − 1 = 0
n
√ o
Ans: −5 ± 26
b. 3x2 − 6x = 10
(
√ )
3 ± 39
Ans:
3
c. x2 − 6x − 8 = 0
n
√ o
Ans: 3 ± 17
d. 2x2 + 3x − 3 = 0
(
√ )
−3 ± 33
Ans:
4
e. x2 + 4x + 1 = 0
n
√ o
Ans: −2 ± 3
4. Solve the equation by using the quadratic formula. Simplify your solution.
a. −2x2 + 3x + 6 = 0
(
√ )
3 ± 57
Ans:
4
b. x2 + 4x + 9 = 0
Ans: No Solution
c. 3x2 + x + 1 = 0
Ans: No Solution
d. −x2 − 3x + 5 = 0
(
√ )
−3 ± 29
Ans:
2
e. 4x2 + x − 4 = 0
(
√ )
−1 ± 65
Ans:
8
5. Solve the equation by any method you like:
a. 9x2 + 2x = 27
(
√ )
−1 ± 2 61
Ans:
9
b. 3x2 + 4x − 2 = 0
(
√ )
−2 ± 10
Ans:
3
c. x2 − 10x + 6 = 0
n
√ o
Ans: 5 ± 19
d. 2x2 + x = −4
Ans: No Solution
e. x2 − x = 6
Ans: {−2, 3}
f. 2x2 + x − 2 = 1
3
Ans: 1, −
2
g. x2 − 7x = 0
Ans: {0, 7}
h. 3x3 − 6x = 7x2
2
Ans: 3, −
3
i. 2x2 + 5x = 12
3
Ans: −4,
2
j. x2 + 2x − 24 = 11
Ans: {5, −7}
k. (x − 1)2 = 48
n
√ o
Ans: 1 ± 4 3
l. (x + 1)2 = 5
n
√ o
Ans: −1 ± 5