document.write( "Question 113449: I need help with my sons Algebra II, it has been many years...\r
\n" ); document.write( "\n" ); document.write( "Solve the inequality algebraically\r
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\n" ); document.write( "\n" ); document.write( "x 2 -3x-4 < 0 (that is x squared) \n" ); document.write( "
Algebra.Com's Answer #82529 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "\"x+%5E2+-3x-4+%3C+0\"\r
\n" ); document.write( "\n" ); document.write( "We need to solve it as an equation and find roots.\r
\n" ); document.write( "\n" ); document.write( "\"x+%5E2+-3x-4+=+0\"\r
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\n" ); document.write( "\n" ); document.write( "Here is the solution with graph:\r
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Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:

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\n" ); document.write( " Starting with the general quadratic
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\n" ); document.write( " \"ax%5E2%2Bbx%2Bc=0\"
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\n" ); document.write( " the general solution using the quadratic equation is:
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\n" ); document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"
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\n" ); document.write( " So lets solve \"x%5E2-3%2Ax-4=0\" ( notice \"a=1\", \"b=-3\", and \"c=-4\")
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\n" ); document.write( " \"x+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29\" Plug in a=1, b=-3, and c=-4
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\n" ); document.write( " \"x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29\" Negate -3 to get 3
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\n" ); document.write( " \"x+=+%283+%2B-+sqrt%28+9-4%2A1%2A-4+%29%29%2F%282%2A1%29\" Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because \"%28-3%29%5E2=-3%2A-3=9\".)
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\n" ); document.write( " \"x+=+%283+%2B-+sqrt%28+9%2B16+%29%29%2F%282%2A1%29\" Multiply \"-4%2A-4%2A1\" to get \"16\"
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\n" ); document.write( " \"x+=+%283+%2B-+sqrt%28+25+%29%29%2F%282%2A1%29\" Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " \"x+=+%283+%2B-+5%29%2F%282%2A1%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
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\n" ); document.write( " \"x+=+%283+%2B-+5%29%2F2\" Multiply 2 and 1 to get 2
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\n" ); document.write( " So now the expression breaks down into two parts
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\n" ); document.write( " \"x+=+%283+%2B+5%29%2F2\" or \"x+=+%283+-+5%29%2F2\"
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\n" ); document.write( " Lets look at the first part:
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\n" ); document.write( " \"x=%283+%2B+5%29%2F2\"
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\n" ); document.write( " \"x=8%2F2\" Add the terms in the numerator
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\n" ); document.write( " \"x=4\" Divide
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\n" ); document.write( " So one answer is
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\n" ); document.write( " \"x=4\"
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\n" ); document.write( " Now lets look at the second part:
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\n" ); document.write( " \"x=%283+-+5%29%2F2\"
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\n" ); document.write( " \"x=-2%2F2\" Subtract the terms in the numerator
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\n" ); document.write( " \"x=-1\" Divide
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\n" ); document.write( " So another answer is
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\n" ); document.write( " \"x=-1\"
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\n" ); document.write( " So our solutions are:
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\n" ); document.write( " \"x=4\" or \"x=-1\"
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\n" ); document.write( "\n" ); document.write( "As you can see, your solutions are: \"x%5B1%5D+=+4\" and \"x%5B2%5D+=+-1\"\r
\n" ); document.write( "\n" ); document.write( "For these values \"x+%5E2+-3x-4\" will be equal to \"+0\". That means for all values of \"x\" from \"-1\" (excluding \"-1\") to \"4\" (excluding \"4\"), you will have \"x+%5E2+-3x-4\" less than \"0\".\r
\n" ); document.write( "\n" ); document.write( "or \"x+%5E2+-3x-4+%3C+0\" for \"-1%3C+x+%3C+4\"\r
\n" ); document.write( "\n" ); document.write( "As you can see on graph, that part of the parabola lies in III-th and IV-th quadrant (under x-axis)\r
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