document.write( "Question 459729: x2 + 4x = 23
\n" ); document.write( " complete the square root . \n" ); document.write( "
Algebra.Com's Answer #315250 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!
\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2+%2B+4x+=+23\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2+%2B+4x-23=0\"\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-23\", first we need to ask ourselves: What two numbers multiply to -23 and add to 4? Lets find out by listing all of the possible factors of -23
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Factors:
\n" ); document.write( "
\n" ); document.write( " 1,23,
\n" ); document.write( "
\n" ); document.write( " -1,-23,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 -23.
\n" ); document.write( "
\n" ); document.write( " (-1)*(23)=-23
\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|-23|1+(-23)=-22
-1|23|(-1)+23=22
\r\n" ); document.write( " \r\n" ); document.write( " None of these factors add to 4. So this quadratic cannot be factored. In order to solve for x, we need to use the quadratic formula.\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "
\n" );