document.write( "Question 862365: Please help so i can learn how to do this! I would really appreciate it........ If twice the square of a positive number is added to the product of -9 and the number, the result is 18. Find the number \n" ); document.write( "
Algebra.Com's Answer #519634 by Theo(13342)\"\" \"About 
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let x = the positive number.
\n" ); document.write( "twice the square of the positive number is therefore equal to 2*x^2.
\n" ); document.write( "the product of -9 and the number is equal to -9*x
\n" ); document.write( "if you add twice the square of the positive number to the product of -9 and the number, the result is 18.
\n" ); document.write( "this becomes:
\n" ); document.write( "2*x^2 + -9*x = 18 which simplifies to:
\n" ); document.write( "2*x^2 - 9*x = 18
\n" ); document.write( "this is a quadratic equation.
\n" ); document.write( "convert it to standard form by subtracting 18 from both sides of the equation to get:
\n" ); document.write( "2x^2 - 9x - 18 = 0
\n" ); document.write( "factor this equation to get:
\n" ); document.write( "(2x + 3) * (x - 6) = 0
\n" ); document.write( "either one of these factors or both have to be equal to 0.
\n" ); document.write( "set each factor equal to 0.
\n" ); document.write( "2x + 3 = 0 results in x = -3/2
\n" ); document.write( "x - 6 = 0 results in x = 6
\n" ); document.write( "since the number has to be positive, x = 6 is the number.
\n" ); document.write( "2 * 6^2 = 2*36 = 72
\n" ); document.write( "-9 * 6 = -54
\n" ); document.write( "72 - 54 = 18
\n" ); document.write( "the solution is confirmed to be good because the original problem statement is true when x is replaced with 6.
\n" ); document.write( "here's a reference you might find helpful.
\n" ); document.write( "http://www.purplemath.com/modules/translat.htm
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