Expert: Sherman D. - 2/2/2006

Question
1.Which equations represent one of the steps of solving 6x^2-6x-12=0 by factoring ?
A)6x+4=0 or x-3=0
B)6x+2=0 or x-6=0
C)2x-x=0 or 3x+6=0
D)x-2=0 or x+1=0
2. Identify the solutions to the equation 2x^2+5x=3 when you solve by factoring.
3.Identify the number that needs to be added to both sides of the equation x^2+4x=96 to complete the square.
4. Identify the solutions to the equation 4x^2-20x=-25 when you solve by completing the square.
5. Identify the solution to the equation x^2-5x=24 when you solve by completing the square.

Answer
1.)
6x^2 - 6x - 12 = 0
6(x^2 - x - 2) = 0
6(x - 2)(x + 1) = 0

ANS : D.) x - 2 = 0 or x + 1 = 0

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2.)
2x^2 + 5x = 3
2x^2 + 5x - 3 = 0
(2x - 1)(x + 3)

ANS : (1/2) or -3

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3.)
x^2 + 4x = 96
find half of 4, square it, and add to both sides
(4/2)^2 = 2^2 = 4
x^2 + 4x + 4 = 100
factor the left side into a perfect square
(x + 2)^2 = 100
sqrt both sides
x + 2 = ±10
subtract 2 from both sides
x = -12 or 8

As you can see the answer is 4. The reason i continued the work is to proove that 4 is the answer.

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4.)
4x^2 - 20x = -25
divide everything by 4
x^2 - 5x = (-25/4)
find half of 5, square it, add to both sides
(5/2)^2 = (25/4)
x^2 - 5x + (25/4) = 0
Factor the left side into a perfect square
(x - (5/2))^2 = 0
sqrt both sides
x - (5/2) = 0
add (5/2) to both sides
x = (5/2)

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5.)
x^2 - 5x = 24
find half of 5, square it, add to both sides
(5/2)^2 = (25/4)
x^2 - 5x + (25/4) = 24 + (25/4)
x^2 - 5x + (25/4) = (96 + 25)/4
x^2 - 5x + (25/4) = (121/4)
factor the left side into a perfect square
(x - (5/2))^2 = (121/4)
sqrt both sides
x - (5/2) = ±(11/2)
add (5/2) to both sides
x = (5/2) ± (11/2)
x = (16/2) or (-6/2)
x = 8 or -3