document.write( "Question 822038: solve for x-values between [0,2pi)
\n" ); document.write( "6sin^2x+9sinx+3=0 \n" ); document.write( "

Algebra.Com's Answer #494590 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"6sin%5E2%28x%29%2B9sin%28x%29%2B3=0\"$
\n" ); document.write( " $\"2sin%5E2%28x%29%2B3sin%28x%29%2B1=0\"$
\n" ); document.write( " $\"%282sin%28x%29%2B1%29%29%28sin%28x%29%2B1%29=0\"$
\n" ); document.write( "Either
\n" ); document.write( " $\"2sin%28x%29%2B1=0\"$ --> $\"2sin%28x%29=-1\"$ --> $\"sin%28x%29=-1%2F2\"$ ,
\n" ); document.write( "or
\n" ); document.write( " $\"sin%28x%29%2B1=0\"$ --> $\"sin%28x%29=-1\"$ .
\n" ); document.write( "
\n" ); document.write( " $\"system%28sin%28x%29=-1%2F2%2C0%3C=x%3C2pi%29\"$ --> $\"system%28highlight%28x=11pi%2F6%29%2C+%22or%22%2Chighlight%28x=7pi%2F6%29%29\"$
\n" ); document.write( "because $\"sin%28pi%2F6%29=1%2F2\"$ --> $\"sin%28-pi%2F6%29=-1%2F2\"$ --> $\"sin%282pi-pi%2F6%29=-1%2F2\"$ --> $\"sin%2811pi%2F6%29=-1%2F2\"$ and
\n" ); document.write( " $\"sin%28pi%2F6%29=1%2F2\"$ --> $\"sin%28pi%2Bpi%2F6%29=-1%2F2\"$ --> $\"sin%287pi%2F6%29=-1%2F2\"$
\n" ); document.write( "
\n" ); document.write( " $\"system%28sin%28x%29=-1%2C0%3C=x%3C2pi%29\"$ --> $\"highlight%28x=pi%29\"$
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\n" ); document.write( "TIP:
\n" ); document.write( "When you get a problem like, you can change variable, or at least think of it that way.
\n" ); document.write( "In this case, if you substitute $\"sin%28x%29=y\"$ the equation transforms into the simple quadratic equation
\n" ); document.write( " $\"6y%5E2%2B9y%2B3=0\"$ .
\n" ); document.write( "It is a lot easier to write, and a lot easier to see how to factor it and solve it.
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