I like to use a fill in the blank method.
1) x^2 - 5x -14
= x^2 - 5x ____ - 14 ____
To find what goes in the first blank, you must take HALF of the middle coefficient (the -5) and SQUARE it. So, half of -5 is -5/2, squared equals 25/4. Now, if you ADD 25/4 in the first blank, you must SUBTRACT it off the second blank. Thus you get...
= x^2 - 5x + 25/4 - 14 - 25/4
From here, the first three terms give a perfect square trinomial, so you can factor it into a binomial squared. The binomial is basically the square root of the first term, and the number you found to be half of the middle coefficient (the -5/2). So, you then get...
= (x - 5/2)^2 - 56/4 - 25/4 = (x - 5/2)^2 - 81/4
For 2), it is basically the same except you need to factor it a bit first...
4x^2 - 8x + 3
= 4(x^2 - 2x____) + 3 ____
Same idea to fill the first blank. Half of -2 is -1, squared equals 1. BUT for the second blank, it is NOT -1. Here's why.. See the 4 you factored out? If you multiply that back in, you really added in 4, not 1, so in the second blank, you need a -4. Thus you get...
= 4(x^2 - 2x + 1) + 3 - 4
= 4(x - 1)^2 - 1
Hope this helps.
2007-06-10 15:53:40
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answer #1
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answered by Lee 3
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1)
x^2 - 5x - 14 = 0
Move the constant.
x^2 - 5x + __ = 14 + __
In the blank: (b/2)^2
x^2 - 5x + 25/4 = 14 + 25/4
Whatever you do to one side, you must do to the other to keep it balanced.
(x - __)^2 = 56/4 + 25/4
In the blank: b/2
(x - (5/2))^2 = 81/4
Solve.
x - (5/2) = +/- root(81/4)
x - 5/2 = +/- (9/2)
x = 9/2 + 5/2 = 14/2 = 7
x = -9/2 + 5/2 = -4/2 = -2
~*~*~*~*~*~*~*~*~*~
2)
4x^2 - 8x + 3 = 0
4x^2 - 8x = -3
4(x^2 - 2x + __) = -3 + __
4(x^2 - 2x + 1) = -3 + 4
4(x - 1)^2 = 1
(x - 1)^2 = 1/4
x - 1 = +/- root(1/4)
x - 1 = +/- (1/2)
x = 1/2 + 2/2 = 3/2
x = -1/2 + 2/2 = 1/2
2007-06-10 15:55:08
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answer #2
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answered by its_victoria08 6
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Question 1
(x² - 5x + 25/4) - 25/4 - 14
(x - 5/2)² - 25/4 - 56/4
(x - 5/2)² - 81/4
(x - 5/2)² - (9/2)²
Question 2
4.[ x² - 2x + 3/4 ]
4.[ (x² - 2x + 1) - 1 + 3/4 ]
4.[ (x - 1)² - 1/4 ]
4.(x - 1)² - 1
2007-06-11 02:34:49
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answer #3
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answered by Como 7
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1)x^2 - 5x - 14
= (x - 2.5)^2 - (2.5)^2 - 14
= (x-2.5)^2 - 20.25
2)4x^2 - 8x + 3
= 4(x^2 - 2x + (3/4))
= 4[(x-1)^2 - 1 + 3/4]
= 4(x-1)^2 -1
2007-06-10 15:45:50
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answer #4
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answered by Kemmy 6
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1)
(x-7)(x+2)
x = 7 OR x = 2
2)
(2x-3)(2x-1)
x = 3/2 OR x = 1/2
2007-06-10 15:48:04
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answer #5
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answered by Anonymous
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1. x^2 - 5x - 14
CAN FACTORED INTO A RADICAL POLYNOMIAL:
(x + 2)(x - 7)
THEREFORE:
x = -2 OR x = 7
2. 4x^2 - 8x + 3
CAN BE FACTORED INTO A RADICAL POLYNOMIAL:
4 (x - 1/2) (x - 3/2)
OR EXPRESSED SIMPLY AS A RATIONALE POLYNOMIAL:
(2x - 1)(2x - 3)
THEREFORE:
x = 1/2 OR x = 3/2
2007-06-10 16:16:13
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answer #6
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answered by Rey Arson II 3
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1) (x-7)(x+2)
x=7 and -2
2) (2x-3)(2x-1)
x=3/2 and 1/2
2007-06-10 15:46:36
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answer #7
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answered by Cool Nerd At Your Service 4
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1) answer: (x - 7) * (x + 2)
2) answer: (2x - 1) * (2x - 3)
2007-06-10 16:30:05
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answer #8
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answered by dat_nguyen160 2
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1) (x-7)(x+2)
2) (2x-3)(2x-1)
2007-06-10 15:46:47
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answer #9
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answered by Anonymous
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1)
(x+2)(x-7)
2)
(2x-1)(2x-3)
2007-06-10 15:47:05
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answer #10
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answered by clz831 2
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