document.write( "Question 1086811: Find all solutions to the equation.\r
\n" ); document.write( "\n" ); document.write( "7 sin^2x - 14 sin x + 2 = -5\r
\n" ); document.write( "\n" ); document.write( "Show all your work. \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #701043 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Use a substitution,
\n" ); document.write( " $\"u=sin%28x%29\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"7u%5E2-14u%2B2=-5\"$
\n" ); document.write( " $\"7u%5E2-14u-7=0\"$
\n" ); document.write( " $\"u%5E2-2u-1=0\"$
\n" ); document.write( "Complete the square,
\n" ); document.write( " $\"%28u%5E2-2u%2B1%29-1=1\"$
\n" ); document.write( " $\"%28u-1%29%5E2=2\"$
\n" ); document.write( " $\"u-1=0+%2B-+sqrt%282%29\"$
\n" ); document.write( " $\"u=1+%2B-+sqrt%282%29\"$
\n" ); document.write( " $\"sin%28x%29=1+%2B-+sqrt%282%29\"$
\n" ); document.write( "The positive solution yields no solutions since $\"sin%28x%29%3C=1\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"sin%28x%29=1-sqrt%282%29\"$
\n" ); document.write( " $\"x=sin%5E%28-1%29%281-sqrt%282%29%29\"$
\n" ); document.write( "Remember there are two solutions.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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