document.write( "Question 684843: \"%282cos%5E2x-3sinx=0\"\r
\n" ); document.write( "\n" ); document.write( "the cos is powered
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Algebra.Com's Answer #424219 by Alan3354(69443)\"\" \"About 
You can put this solution on YOUR website!
\"2cos%5E2%28x%29+-+3sin%28x%29=0\"
\n" ); document.write( "cos^2 = 1 - sin^2
\n" ); document.write( "\"2%281+-+sin%5E2%28x%29%29+-+3sin%28x%29=0\"
\n" ); document.write( "\"2sin%5E2%28x%29+%2B+3sin%28x%29+-+2+=+0\"
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\n" ); document.write( "sub y for sin(x)
\n" ); document.write( "\"2y%5E+%2B+3y+-+2+=+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 \"2x%5E2%2B3x%2B-2+=+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=%283%29%5E2-4%2A2%2A-2=25\".
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\n" ); document.write( " Discriminant d=25 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-3%2B-sqrt%28+25+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%283%29%2Bsqrt%28+25+%29%29%2F2%5C2+=+0.5\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%283%29-sqrt%28+25+%29%29%2F2%5C2+=+-2\"
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\n" ); document.write( " Quadratic expression \"2x%5E2%2B3x%2B-2\" can be factored:
\n" ); document.write( " \"2x%5E2%2B3x%2B-2+=+%28x-0.5%29%2A%28x--2%29\"
\n" ); document.write( " Again, the answer is: 0.5, -2.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B3%2Ax%2B-2+%29\"

\n" ); document.write( "\n" ); document.write( "sin(x) = -2, ignore, no real numbers.
\n" ); document.write( "sin(x) = 0.5
\n" ); document.write( "x = pi/6 + 2n*pi, n = 0,1,2,3
\n" ); document.write( "x = 5pi/6 + 2n*pi, n = 0,1,2,3
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