document.write( "Question 490779: AGAIN, I'm getting stuck here! Right when I thought I knew it...\r
\n" ); document.write( "\n" ); document.write( "Solve 6x^2 + 3x – 12 = 2 – 2x\r
\n" ); document.write( "\n" ); document.write( "Okay, so I subtracted 2-2x from both sides and end up with 6x^2+5x-14
\n" ); document.write( "Now, do I divide by 6? I don't understand how that would work, and there are no factors of 14. I'm looking at my teacher's notes from last year and they aren't helping. \n" ); document.write( "

Algebra.Com's Answer #334303 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Looking at the expression $\"6x%5E2%2B5x-14\"$ , we can see that the first coefficient is $\"6\"$ , the second coefficient is $\"5\"$ , and the last term is $\"-14\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"6\"$ by the last term $\"-14\"$ to get $\"%286%29%28-14%29=-84\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-84\"$ (the previous product) and add to the second coefficient $\"5\"$ ?\r
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\n" ); document.write( "\n" ); document.write( "To find these two numbers, we need to list all of the factors of $\"-84\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-84\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,7,12,14,21,28,42,84\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-7,-12,-14,-21,-28,-42,-84\r
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\n" ); document.write( "\n" ); document.write( "Note: list the negative of each factor. This will allow us to find all possible combinations.\r
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\n" ); document.write( "\n" ); document.write( "These factors pair up and multiply to $\"-84\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-84) = -84
\n" ); document.write( "2*(-42) = -84
\n" ); document.write( "3*(-28) = -84
\n" ); document.write( "4*(-21) = -84
\n" ); document.write( "6*(-14) = -84
\n" ); document.write( "7*(-12) = -84
\n" ); document.write( "(-1)*(84) = -84
\n" ); document.write( "(-2)*(42) = -84
\n" ); document.write( "(-3)*(28) = -84
\n" ); document.write( "(-4)*(21) = -84
\n" ); document.write( "(-6)*(14) = -84
\n" ); document.write( "(-7)*(12) = -84\r
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\n" ); document.write( "\n" ); document.write( "Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"5\"$ :\r
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First Number	Second Number	Sum
1	-84	1+(-84)=-83
2	-42	2+(-42)=-40
3	-28	3+(-28)=-25
4	-21	4+(-21)=-17
6	-14	6+(-14)=-8
7	-12	7+(-12)=-5
-1	84	-1+84=83
-2	42	-2+42=40
-3	28	-3+28=25
-4	21	-4+21=17
-6	14	-6+14=8
-7	12	-7+12=5

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-7\"$ and $\"12\"$ add to $\"5\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-7\"$ and $\"12\"$ both multiply to $\"-84\"$ and add to $\"5\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"5x\"$ with $\"-7x%2B12x\"$ . Remember, $\"-7\"$ and $\"12\"$ add to $\"5\"$ . So this shows us that $\"-7x%2B12x=5x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"6x%5E2%2Bhighlight%28-7x%2B12x%29-14\"$ Replace the second term $\"5x\"$ with $\"-7x%2B12x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%286x%5E2-7x%29%2B%2812x-14%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%286x-7%29%2B%2812x-14%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%286x-7%29%2B2%286x-7%29\"$ Factor out $\"2\"$ from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B2%29%286x-7%29\"$ Combine like terms. Or factor out the common term $\"6x-7\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"6x%5E2%2B5x-14\"$ factors to $\"%28x%2B2%29%286x-7%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"6x%5E2%2B5x-14=%28x%2B2%29%286x-7%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%28x%2B2%29%286x-7%29\"$ to get $\"6x%5E2%2B5x-14\"$ or by graphing the original expression and the answer (the two graphs should be identical).\r
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\n" ); document.write( "\n" ); document.write( "I'll let you take it from here.\r
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\n" ); document.write( "\n" ); document.write( "If you need more help, feel free to email me at
\n" ); document.write( "jim_thompson5910@hotmail.com\r
\n" ); document.write( "\n" ); document.write( "Thanks,\r
\n" ); document.write( "\n" ); document.write( "Jim \n" ); document.write( "

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