document.write( "Question 79679: The square of a number decreased by 2 is equal to the negative of the number. Find the number. \n" ); document.write( "
Algebra.Com's Answer #57171 by ankor@dixie-net.com(22740)\"\" \"About 
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The square of a number decreased by 2 is equal to the negative of the number. Find the number.
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\n" ); document.write( "Let \"a number\" = x
\n" ); document.write( "Squared: x^2
\n" ); document.write( "decreased by 2: (x^2 - 2)
\n" ); document.write( "negative of the number: -x
\n" ); document.write( ":
\n" ); document.write( " x^2 - 2 = -x
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\n" ); document.write( " add x to both sides, you then have a quadratic equation:
\n" ); document.write( "x^2 + x - 2 = 0
\n" ); document.write( ":
\n" ); document.write( "Factors to:
\n" ); document.write( "(x + 2)(x - 1) = 0
\n" ); document.write( ":
\n" ); document.write( "x = -2;
\n" ); document.write( "and
\n" ); document.write( "x = +1
\n" ); document.write( ":
\n" ); document.write( "Check using x = -2 in the original equation:
\n" ); document.write( "(-2)^2 + (-2) = -(-2)
\n" ); document.write( "+4 - 2 = +2
\n" ); document.write( ":
\n" ); document.write( "Check using x = +1
\n" ); document.write( "(1^2) - 2 = -1
\n" ); document.write( " 1 - 2 = -1\r
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