document.write( "Question 194972: How would you solve problems like:
\n" ); document.write( "x^2+5=0
\n" ); document.write( "x^2-11=0\r
\n" ); document.write( "\n" ); document.write( "Why is there two solutions?\r
\n" ); document.write( "\n" ); document.write( "Thank you \n" ); document.write( "
Algebra.Com's Answer #146250 by Alan3354(69443)\"\" \"About 
You can put this solution on YOUR website!
How would you solve problems like:
\n" ); document.write( "x^2+5=0
\n" ); document.write( "x^2-11=0
\n" ); document.write( "Why is there two solutions?
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\n" ); document.write( "x^2+5=0
\n" ); document.write( "Since there's no x term:
\n" ); document.write( "\"x%5E2+=+-5\"
\n" ); document.write( "x = ± i*sqrt(5) where i = sqrt(-1)
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\n" ); document.write( "x^2-11=0
\n" ); document.write( "\"x%5E2+=+11\"
\n" ); document.write( "x = +sqrt(11)
\n" ); document.write( "x = -sqrt(11)
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\n" ); document.write( "There are 2 solutions because both work.
\n" ); document.write( "In the 2nd eqn, both +sqrt(11) and -sqrt(11) are 11 when they're multiplied by themselves.
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B0x%2B-11+=+0\") has the following solutons:
\n" ); document.write( "
\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
\n" ); document.write( "
\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
\n" ); document.write( "
\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%280%29%5E2-4%2A1%2A-11=44\".
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\n" ); document.write( " Discriminant d=44 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-0%2B-sqrt%28+44+%29%29%2F2%5Ca\".
\n" ); document.write( "
\n" ); document.write( " \"x%5B1%5D+=+%28-%280%29%2Bsqrt%28+44+%29%29%2F2%5C1+=+3.3166247903554\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%280%29-sqrt%28+44+%29%29%2F2%5C1+=+-3.3166247903554\"
\n" ); document.write( "
\n" ); document.write( " Quadratic expression \"1x%5E2%2B0x%2B-11\" can be factored:
\n" ); document.write( " \"1x%5E2%2B0x%2B-11+=+%28x-3.3166247903554%29%2A%28x--3.3166247903554%29\"
\n" ); document.write( " Again, the answer is: 3.3166247903554, -3.3166247903554.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B-11+%29\"

\n" ); document.write( "\n" ); document.write( "-------
\n" ); document.write( "If you graph them, you'll see that they cross the x-axis in 2 places (the 2nd one).
\n" ); document.write( "You can get FREE software to graph these at
\n" ); document.write( "www.padowan.dk.com/graph/
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