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2 problems, complete the square. thank you!

1)x^2 - 5x - 14

2)4x^2 - 8x + 3

2007-06-10 15:41:12 · 10 answers · asked by poker22only 2 in Science & Mathematics Mathematics

10 answers

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 · answer #1 · answered by Lee 3 · 1 0

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 · answer #2 · answered by its_victoria08 6 · 0 0

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 · answer #3 · answered by Como 7 · 0 0

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 · answer #4 · answered by Kemmy 6 · 1 1

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 · answer #5 · answered by Anonymous · 0 1

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 · answer #6 · answered by Rey Arson II 3 · 0 0

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 · answer #7 · answered by Cool Nerd At Your Service 4 · 0 2

1) answer: (x - 7) * (x + 2)
2) answer: (2x - 1) * (2x - 3)

2007-06-10 16:30:05 · answer #8 · answered by dat_nguyen160 2 · 0 0

1) (x-7)(x+2)
2) (2x-3)(2x-1)

2007-06-10 15:46:47 · answer #9 · answered by Anonymous · 0 2

1)

(x+2)(x-7)

2)

(2x-1)(2x-3)

2007-06-10 15:47:05 · answer #10 · answered by clz831 2 · 0 2

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