document.write( "Question 235794: Hi.\r
\n" ); document.write( "\n" ); document.write( "I have been trying for over an hour and can not
\n" ); document.write( "solve the following polynomial inequality.\r
\n" ); document.write( "\n" ); document.write( "\"+x%5E2%2B5x%3C=3+\"\r
\n" ); document.write( "\n" ); document.write( "Correct answer is given: [-3,1]\r
\n" ); document.write( "\n" ); document.write( "Thank you in advance
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Algebra.Com's Answer #173677 by Alan3354(69443)\"\" \"About 
You can put this solution on YOUR website!
\"+x%5E2%2B5x%3C=3+\"
\n" ); document.write( "Solve it as equal, then add the <
\n" ); document.write( "\"+x%5E2%2B5x%3C=3+\"
\n" ); document.write( "\"+x%5E2%2B5x-3=0+\"
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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%2B5x%2B-3+=+0\") has the following solutons:
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\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%285%29%5E2-4%2A1%2A-3=37\".
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\n" ); document.write( " Discriminant d=37 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-5%2B-sqrt%28+37+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%285%29%2Bsqrt%28+37+%29%29%2F2%5C1+=+0.54138126514911\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%285%29-sqrt%28+37+%29%29%2F2%5C1+=+-5.54138126514911\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B5x%2B-3\" can be factored:
\n" ); document.write( " \"1x%5E2%2B5x%2B-3+=+%28x-0.54138126514911%29%2A%28x--5.54138126514911%29\"
\n" ); document.write( " Again, the answer is: 0.54138126514911, -5.54138126514911.\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%2B5%2Ax%2B-3+%29\"

\n" ); document.write( "\n" ); document.write( "Sub <= for the equal signs.
\n" ); document.write( "All values between the 2 solutions fit the inequality.
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\n" ); document.write( "It's not -3 and 1.
\n" ); document.write( "For the solution to be -3 and 1:
\n" ); document.write( "\"x%5E2+%2B+2x+%3C=3\"
\n" ); document.write( "--> -3>=x>=1
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