document.write( "Question 77047This question is from textbook Glencoe Algebra 1
\n" ); document.write( ": \"a%5E2%2B13a%2B36=0\" \n" ); document.write( "
Algebra.Com's Answer #55217 by jim_thompson5910(35256)\"\" \"About 
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Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor \"1%2Ax%5E2%2B13%2Ax%2B36\", first we need to ask ourselves: What two numbers multiply to 36 and add to 13? Lets find out by listing all of the possible factors of 36
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\n" ); document.write( " Factors:
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\n" ); document.write( " 1,2,3,4,6,9,12,18,36,
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\n" ); document.write( " -1,-2,-3,-4,-6,-9,-12,-18,-36,List the negative factors as well. This will allow us to find all possible combinations
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\n" ); document.write( " These factors pair up to multiply to 36.
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\n" ); document.write( " 1*36=36
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\n" ); document.write( " 2*18=36
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\n" ); document.write( " 3*12=36
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\n" ); document.write( " 4*9=36
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\n" ); document.write( " 6*6=36
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\n" ); document.write( " (-1)*(-36)=36
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\n" ); document.write( " (-2)*(-18)=36
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\n" ); document.write( " (-3)*(-12)=36
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\n" ); document.write( " (-4)*(-9)=36
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\n" ); document.write( " (-6)*(-6)=36
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\n" ); document.write( " note: remember two negative numbers multiplied together make a positive number
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\n" ); document.write( " Now which of these pairs add to 13? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 13
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First Number|Second Number|Sum
1|36|1+36=37
2|18|2+18=20
3|12|3+12=15
4|9|4+9=13
6|6|6+6=12
-1|-36|-1+(-36)=-37
-2|-18|-2+(-18)=-20
-3|-12|-3+(-12)=-15
-4|-9|-4+(-9)=-13
-6|-6|-6+(-6)=-12
We can see from the table that 4 and 9 add to 13. So the two numbers that multiply to 36 and add to 13 are: 4 and 9\r\n" ); document.write( " \r\n" ); document.write( " Now we substitute these numbers into a and b of the general equation of a product of linear factors which is:\r\n" ); document.write( " \r\n" ); document.write( " \"%28x%2Ba%29%28x%2Bb%29\"substitute a=4 and b=9\r\n" ); document.write( " \r\n" ); document.write( " So the equation becomes:\r\n" ); document.write( " \r\n" ); document.write( " (x+4)(x+9)\r\n" ); document.write( " \r\n" ); document.write( " \r\n" ); document.write( " Notice that if we foil (x+4)(x+9) we get the quadratic \"1%2Ax%5E2%2B13%2Ax%2B36\" again\n" ); document.write( "

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\n" ); document.write( "\n" ); document.write( "Just replace the x's with a's to get:\r
\n" ); document.write( "\n" ); document.write( "\"%28a%2B4%29%28a%2B9%29=0\"\r
\n" ); document.write( "\n" ); document.write( "Set each term to zero\r
\n" ); document.write( "\n" ); document.write( "\"a%2B4=0\"
\n" ); document.write( "\"a=-4\"\r
\n" ); document.write( "\n" ); document.write( "\"a%2B9=0\"
\n" ); document.write( "\"a=-9\"\r
\n" ); document.write( "\n" ); document.write( "So our answer is
\n" ); document.write( "\"a=-4\" or \"a=-9\" \n" ); document.write( "
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