document.write( "Question 859644: If three is added to twice the square of an integer, the result is equal to seven times the integer. Find the integer. \n" ); document.write( "

Algebra.Com's Answer #517890 by DrBeeee(684) $\"\"$ $\"About$

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Let n = the integer
\n" ); document.write( "The problem statement gives us
\n" ); document.write( "(1) 3 + 2*n^2 = 7*n or
\n" ); document.write( "(2) 2*n^2 - 7*n + 3 = 0 which factors to
\n" ); document.write( "(3) (2n - 1)*(n - 3) = 0
\n" ); document.write( "Set each factor equal to zero and solve for n gives us
\n" ); document.write( "(4) n = 1/2,3
\n" ); document.write( "Since n is an integer we select
\n" ); document.write( "(5) n = 3
\n" ); document.write( "Check this with (1).
\n" ); document.write( "Is (3 + 2*3^2 = 7*3)?
\n" ); document.write( "Is (3 + 2*9 = 21)?
\n" ); document.write( "Is (3 + 18 = 21)?
\n" ); document.write( "Is (21 = 21)? Yes
\n" ); document.write( "Answer: The integer is 3.
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