Answer:
Step-by-step explanation:
1. x² + 8x + 15 = 0
Think of the factors of 15 that when added will have a sum of 8
15 = 1,3,5,15
x² + 8x + 15 = 0
(x + 3)(x + 5) = 0
x + 3 = 0
x = -3
x + 5 = 0
x = -5
x = -3,
2. x² - 7x + 12 = 0
factors of 12 that when added will have a sum of -7
12 = -1,-2,-3,-4,-6, -12
(x -3)(x - 4) = 0
x - 3 = 0
x = 3
x - 4 = 0
x = 4
3. x² + 2x - 15 = 0
factors of -15 that will add up to 2
-15 = -1,-3,5, 15
(x + 5)(x - 3) = 0
4. x² - 11x + 28 = 0
factors of 28 that has a sum of -11
28 = -1,-2,-4,-7,-14, -28
(X - 4)(X - 7) = 0
x - 7 = 0
x = 7
5. x² - x - 30 = 0
factors of -30 that when added will have a sum of -1
-30 = -1,-2,-3,-5,6,10,15,30
-30 = 1,2,3,5, -6, -10, -15, -30
(x + 5)(x - 6) = 0
x -6 = 0
x = 6
6. x² + 11x -26 = 0
-26 = -1,-2,13, 26
(x - 2)(x +13) = 0
x - 2 = 0
x = 2
x + 13 = 0
x = -13
7. x² - 5x - 24 = 0
get the factors
-24 = 1,2,3,4, -6, -8, -12 -24
(x + 3)(x - 8) = 0
x - 8 = 0
x = 8
8. 14 + x² + 9x = 0
rearrange
x² + 9x + 14 = 0
14 = 1, 2, 7, 14
(x + 2)(x + 7) = 0
x + 2 = 0
x = -2
x + 7 = 0
x = -7
9. 7 + x² - 18x = -25
x² - 18x + 7 + 25 = 0
x² - 18x + 32 = 0
get the factors of 32
32 = -1, -2, -4, -8, -16, -32
(x - 2 )(x - 16) = 0
x - 16 = 0
x = 16
10. x² = 17x - 72
x² - 17x + 72 = 0
get the factors of 72
72 = -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -36, -72
(x - 8)(x -9) = 0
x - 9 = 0
x = 9
1. x² - 9 = 0
factors of -9 of which when added will be zero
-9 = 1, 3, -3, -9
x² - 9 = 0
(x + 3)(x - 3) = 0
2. x² - 121 = 0
121 is a perfect square of 11
This follows the difference of perfect squares
(x + 11)(x - 11) = 0
x + 11 = 0
x = -11
x - 11 = 0
x = 11
3. x² - 49 = 0
49 is the perfect square of 7
(x + 7)(x - 7) = 0
4. 2x² - 128 = 0
Divide the whole equation by 2
x² - 64 = 0
64 is the perfect square of 8
(x + 8)(x - 8) = 0
x + 8 = 0
x = -8
5. 4x² - 64 = 0
Divide the whole equation by 4
x² - 16 = 0
16 is the perfect square of 4
(x + 4)(x - 4) = 0
x + 4 = 0
x = -4
x - 4 =0
6. x² - 20 = 5
x² - 20 -5 = 0
x² - 25 = 0
25 is the perfect square of 5
(x +5)(x - 5) = 0
x +5 = 0
x -5 = 0
x = 5
7. X² - 101 = -1
x² - 101 + 1 = 0
x² - 100 = 0
100 is the perfect square of 10
(x + 10)(x - 10) = 0
x +10 = 0
x = -10
x - 10 = 0
x = 10
8. 4x² - 17 = -1
4x² - 17 + 1 = 0
4x² - 16 = 0
divide the whole equation by 4
x² - 4 = 0
4 is the perfect square of 2
(x + 2)(x - 2) = 0
x -2 = 0
9. 3x² - 16 = 227
3x² - 16 -227 = 0
3x² - 243 = 0
divide the whole equation by 3
x² - 81 = 0
81 is the perfect square of 9
(x +9)(x - 9) = 0
x + 9 = 0
x = -9
10. 3x² - 55 = 53
3x² - 55 - 53 = 0
3x² - 108 = 0
x² - 36 = 0
36 is the perfect square of 6
(x + 6)(x - 6) = 0
x + 6 = 0
x = -6
x - 6 = 0
1. 2x² + 15x + 25 = 0
get the factors of 25
25 = 1, 5, 25
(2x + 5)(x + 5) = 0
2x + 5 = 0
2x = -5
x = -5/2
2. 2x² -7x - 15 = 0
Get the factors of 15
15 = 1, 3, -5, -15
(2x + 3)(x -5) = 0
2x + 3 = 0
2x = -3
x = -3/2
x - 5 = 0
3. 3x² + 14x - 24 = 0
get the factors of 24
24 = -1, -2, -3, -4, 6, 8, 12, 24
(3x - 4 )( x + 6) = 0
3x - 4 = 0
3x = 4
x = 4/3
4. 12x² - 28x - 5 = 0
factors of -5
-5 = 1, -5
-5 = -1, 5
(2x -5)(6x +1) = 0
2x - 5 = 0
2x = 5
x = 5/2
6x + 1 = 0
6x = -1
x = -1/6
5. 28x² - 85x + 63 = 0
Get the factors of 63
(4x - 7)(7x - 9) = 0
4x - 7 = 0
4x = 7
x = 7/4
7x - 9 = 0
7x = 9
x = 9/7
x =9/7
6. 19x - 12 - 5x² = 0
transpose
5x² - 19x + 12 = 0
(x - 3)(5x - 4) = 0
5x - 4 = 0
5x = 4
x = 4/5
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Answers & Comments
Verified answer
Answer:
Step-by-step explanation:
1. x² + 8x + 15 = 0
Think of the factors of 15 that when added will have a sum of 8
15 = 1,3,5,15
x² + 8x + 15 = 0
(x + 3)(x + 5) = 0
x + 3 = 0
x = -3
x + 5 = 0
x = -5
x = -3,
x = -5
2. x² - 7x + 12 = 0
factors of 12 that when added will have a sum of -7
12 = -1,-2,-3,-4,-6, -12
(x -3)(x - 4) = 0
x - 3 = 0
x = 3
x - 4 = 0
x = 4
x = 3
x = 4
3. x² + 2x - 15 = 0
factors of -15 that will add up to 2
-15 = -1,-3,5, 15
(x + 5)(x - 3) = 0
x + 5 = 0
x = -5
x - 3 = 0
x = 3
x = -5
x = 3
4. x² - 11x + 28 = 0
factors of 28 that has a sum of -11
28 = -1,-2,-4,-7,-14, -28
(X - 4)(X - 7) = 0
x - 4 = 0
x = 4
x - 7 = 0
x = 7
x = 4
x = 7
5. x² - x - 30 = 0
factors of -30 that when added will have a sum of -1
-30 = -1,-2,-3,-5,6,10,15,30
-30 = 1,2,3,5, -6, -10, -15, -30
(x + 5)(x - 6) = 0
x + 5 = 0
x = -5
x -6 = 0
x = 6
x = -5
x = 6
6. x² + 11x -26 = 0
-26 = -1,-2,13, 26
(x - 2)(x +13) = 0
x - 2 = 0
x = 2
x + 13 = 0
x = -13
x = 2
x = -13
7. x² - 5x - 24 = 0
get the factors
-24 = 1,2,3,4, -6, -8, -12 -24
(x + 3)(x - 8) = 0
x + 3 = 0
x = -3
x - 8 = 0
x = 8
x = -3
x = 8
8. 14 + x² + 9x = 0
rearrange
x² + 9x + 14 = 0
get the factors
14 = 1, 2, 7, 14
(x + 2)(x + 7) = 0
x + 2 = 0
x = -2
x + 7 = 0
x = -7
x = -2
x = -7
9. 7 + x² - 18x = -25
x² - 18x + 7 + 25 = 0
x² - 18x + 32 = 0
get the factors of 32
32 = -1, -2, -4, -8, -16, -32
(x - 2 )(x - 16) = 0
x - 2 = 0
x = 2
x - 16 = 0
x = 16
x = 2
x = 16
10. x² = 17x - 72
x² - 17x + 72 = 0
get the factors of 72
72 = -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -36, -72
(x - 8)(x -9) = 0
x - 8 = 0
x = 8
x - 9 = 0
x = 9
x = 8
x = 9
1. x² - 9 = 0
factors of -9 of which when added will be zero
-9 = 1, 3, -3, -9
x² - 9 = 0
(x + 3)(x - 3) = 0
x + 3 = 0
x = -3
x - 3 = 0
x = 3
x = 3
x = -3
2. x² - 121 = 0
121 is a perfect square of 11
This follows the difference of perfect squares
(x + 11)(x - 11) = 0
x + 11 = 0
x = -11
x - 11 = 0
x = 11
x = 11
x = -11
3. x² - 49 = 0
49 is the perfect square of 7
(x + 7)(x - 7) = 0
x + 7 = 0
x = -7
x - 7 = 0
x = 7
x = 7
x = -7
4. 2x² - 128 = 0
Divide the whole equation by 2
x² - 64 = 0
64 is the perfect square of 8
(x + 8)(x - 8) = 0
x + 8 = 0
x = -8
x - 8 = 0
x = 8
x = 8
x = -8
5. 4x² - 64 = 0
Divide the whole equation by 4
x² - 16 = 0
16 is the perfect square of 4
(x + 4)(x - 4) = 0
x + 4 = 0
x = -4
x - 4 =0
x = 4
x = 4
x = -4
6. x² - 20 = 5
x² - 20 -5 = 0
x² - 25 = 0
25 is the perfect square of 5
(x +5)(x - 5) = 0
x +5 = 0
x = -5
x -5 = 0
x = 5
x = 5
x = -5
7. X² - 101 = -1
x² - 101 + 1 = 0
x² - 100 = 0
100 is the perfect square of 10
(x + 10)(x - 10) = 0
x +10 = 0
x = -10
x - 10 = 0
x = 10
x = 10
x = -10
8. 4x² - 17 = -1
4x² - 17 + 1 = 0
4x² - 16 = 0
divide the whole equation by 4
x² - 4 = 0
4 is the perfect square of 2
(x + 2)(x - 2) = 0
x + 2 = 0
x = -2
x -2 = 0
x = 2
x = 2
x = -2
9. 3x² - 16 = 227
3x² - 16 -227 = 0
3x² - 243 = 0
divide the whole equation by 3
x² - 81 = 0
81 is the perfect square of 9
(x +9)(x - 9) = 0
x + 9 = 0
x = -9
x - 9 = 0
x = 9
x = 9
x = -9
10. 3x² - 55 = 53
3x² - 55 - 53 = 0
3x² - 108 = 0
divide the whole equation by 3
x² - 36 = 0
36 is the perfect square of 6
(x + 6)(x - 6) = 0
x + 6 = 0
x = -6
x - 6 = 0
x = 6
x = 6
x = -6
1. 2x² + 15x + 25 = 0
get the factors of 25
25 = 1, 5, 25
(2x + 5)(x + 5) = 0
2x + 5 = 0
2x = -5
x = -5/2
x + 5 = 0
x = -5
x = -5/2
x = -5
2. 2x² -7x - 15 = 0
Get the factors of 15
15 = 1, 3, -5, -15
(2x + 3)(x -5) = 0
2x + 3 = 0
2x = -3
x = -3/2
x - 5 = 0
x = 5
x = -3/2
x = 5
3. 3x² + 14x - 24 = 0
get the factors of 24
24 = -1, -2, -3, -4, 6, 8, 12, 24
(3x - 4 )( x + 6) = 0
3x - 4 = 0
3x = 4
x = 4/3
x + 6 = 0
x = -6
x = 4/3
x = -6
4. 12x² - 28x - 5 = 0
factors of -5
-5 = 1, -5
-5 = -1, 5
(2x -5)(6x +1) = 0
2x - 5 = 0
2x = 5
x = 5/2
6x + 1 = 0
6x = -1
x = -1/6
x = 5/2
x = -1/6
5. 28x² - 85x + 63 = 0
Get the factors of 63
(4x - 7)(7x - 9) = 0
4x - 7 = 0
4x = 7
x = 7/4
7x - 9 = 0
7x = 9
x = 9/7
x = 7/4
x =9/7
6. 19x - 12 - 5x² = 0
transpose
5x² - 19x + 12 = 0
get the factors
(x - 3)(5x - 4) = 0
x - 3 = 0
x = 3
5x - 4 = 0
5x = 4
x = 4/5
x = 3
x = 4/5