document.write( "Question 78063: In this question the paper gives you a description and you're to put it into a quadratic equation.\r
\n" ); document.write( "\n" ); document.write( "The sum of the square of a number and 4 times the number is 12. \r
\n" ); document.write( "\n" ); document.write( "The equation I got was x^2+4x=12 I'm not sure if it's right but that's what I got. When I went to solve it though I didn't get what my teacher told me I would get, I didn't get two numbers in the end because the square root of the number I got was a decimal and she said we would get whole numbers. Can anyone help? \n" ); document.write( "
Algebra.Com's Answer #55967 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"x%5E2%2B4x=12\" Start with the given equation\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B4x-12=0\" Subtract 12 from both sides\r
\n" ); document.write( "\n" ); document.write( "Factor the quadratic;\r
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor \"1%2Ax%5E2%2B4%2Ax%2B-12\", first we need to ask ourselves: What two numbers multiply to -12 and add to 4? Lets find out by listing all of the possible factors of -12
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Factors:
\n" ); document.write( "
\n" ); document.write( " 1,2,3,4,6,12,
\n" ); document.write( "
\n" ); document.write( " -1,-2,-3,-4,-6,-12,List the negative factors as well. This will allow us to find all possible combinations
\n" ); document.write( "
\n" ); document.write( " These factors pair up to multiply to -12.
\n" ); document.write( "
\n" ); document.write( " (-1)*(12)=-12
\n" ); document.write( "
\n" ); document.write( " (-2)*(6)=-12
\n" ); document.write( "
\n" ); document.write( " (-3)*(4)=-12
\n" ); document.write( "
\n" ); document.write( " Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4
\n" ); document.write( "
\n" ); document.write( " ||||||
First Number|Second Number|Sum
1|-12|1+(-12)=-11
2|-6|2+(-6)=-4
3|-4|3+(-4)=-1
-1|12|(-1)+12=11
-2|6|(-2)+6=4
-3|4|(-3)+4=1
We can see from the table that -2 and 6 add to 4.So the two numbers that multiply to -12 and add to 4 are: -2 and 6\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=-2 and b=6\r\n" ); document.write( " \r\n" ); document.write( " So the equation becomes:\r\n" ); document.write( " \r\n" ); document.write( " (x-2)(x+6)\r\n" ); document.write( " \r\n" ); document.write( " Notice that if we foil (x-2)(x+6) we get the quadratic \"1%2Ax%5E2%2B4%2Ax%2B-12\" again\n" ); document.write( "

\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So you get\r
\n" ); document.write( "\n" ); document.write( "\"%28x-2%29%28x%2B6%29=0\"\r
\n" ); document.write( "\n" ); document.write( "Set each equation equal to zero and solve for x\r
\n" ); document.write( "\n" ); document.write( "\"x-2=0\" or \"x%2B6=0\" \r
\n" ); document.write( "\n" ); document.write( "So our solution is:\r
\n" ); document.write( "\n" ); document.write( "\"x=2\" or \"x=-6\"
\n" ); document.write( " \n" ); document.write( "
\n" );