document.write( "Question 184824: Any help with these three would be appreciated. I keep thinking I've done them correctly but was actually wrong and I've gone around with them so much I think I've completely forgotten what I'm doing!\r
\n" ); document.write( "\n" ); document.write( "1. 3x2 + 11x – 20 = 0 Solve by factoring\r
\n" ); document.write( "\n" ); document.write( "2. x2 + 3x - 4 = 0 Solve by completing the squares\r
\n" ); document.write( "\n" ); document.write( "3. 3x2 – x – 1 = 0 Solve by graphing (preferably using Excel)
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Algebra.Com's Answer #138684 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'll do the first one to get you started. If you're still stuck, then feel free to repost\r
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\n" ); document.write( "\n" ); document.write( "First, let's factor the left side $\"3x%5E2%2B11x-20\"$ :\r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"3x%5E2%2B11x-20\"$ , we can see that the first coefficient is $\"3\"$ , the second coefficient is $\"11\"$ , and the last term is $\"-20\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"3\"$ by the last term $\"-20\"$ to get $\"%283%29%28-20%29=-60\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-60\"$ (the previous product) and add to the second coefficient $\"11\"$ ?\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 $\"-60\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-60\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,5,6,10,12,15,20,30,60\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60\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 $\"-60\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-60)
\n" ); document.write( "2*(-30)
\n" ); document.write( "3*(-20)
\n" ); document.write( "4*(-15)
\n" ); document.write( "5*(-12)
\n" ); document.write( "6*(-10)
\n" ); document.write( "(-1)*(60)
\n" ); document.write( "(-2)*(30)
\n" ); document.write( "(-3)*(20)
\n" ); document.write( "(-4)*(15)
\n" ); document.write( "(-5)*(12)
\n" ); document.write( "(-6)*(10)\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 $\"11\"$ :\r
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First Number	Second Number	Sum
1	-60	1+(-60)=-59
2	-30	2+(-30)=-28
3	-20	3+(-20)=-17
4	-15	4+(-15)=-11
5	-12	5+(-12)=-7
6	-10	6+(-10)=-4
-1	60	-1+60=59
-2	30	-2+30=28
-3	20	-3+20=17
-4	15	-4+15=11
-5	12	-5+12=7
-6	10	-6+10=4

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-4\"$ and $\"15\"$ add to $\"11\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-4\"$ and $\"15\"$ both multiply to $\"-60\"$ and add to $\"11\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"11x\"$ with $\"-4x%2B15x\"$ . Remember, $\"-4\"$ and $\"15\"$ add to $\"11\"$ . So this shows us that $\"-4x%2B15x=11x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"3x%5E2%2Bhighlight%28-4x%2B15x%29-20\"$ Replace the second term $\"11x\"$ with $\"-4x%2B15x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%283x%5E2-4x%29%2B%2815x-20%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%283x-4%29%2B%2815x-20%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%283x-4%29%2B5%283x-4%29\"$ Factor out $\"5\"$ 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( " $\"%28x%2B5%29%283x-4%29\"$ Combine like terms. Or factor out the common term $\"3x-4\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"3x%5E2%2B11x-20\"$ factors to $\"%28x%2B5%29%283x-4%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "This means that $\"3x%5E2%2B11x-20=0\"$ transforms into $\"%28x%2B5%29%283x-4%29=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B5%29%283x-4%29=0\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "Now set each factor equal to zero:\r
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\n" ); document.write( "\n" ); document.write( " $\"x%2B5=0\"$ or $\"3x-4=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "Let's solve the first equation $\"x%2B5=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x=-5\"$ Subtract 5 from both sides to isolate \"x\". \r
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\n" ); document.write( "\n" ); document.write( "So the first solution is $\"x=-5\"$ \r
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\n" ); document.write( "\n" ); document.write( "--------\r
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\n" ); document.write( "\n" ); document.write( "Now let's solve the second equation $\"3x-4=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"3x=4\"$ Add 4 to both sides.\r
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\n" ); document.write( "\n" ); document.write( " $\"x=4%2F3\"$ Divide both sides by 3 to isolate \"x\".\r
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\n" ); document.write( "\n" ); document.write( "So the second solution is $\"x=4%2F3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So the solutions are \r
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\n" ); document.write( "\n" ); document.write( " $\"x=-5\"$ or $\"x=4%2F3\"$ \n" ); document.write( "

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