document.write( "Question 73068: how do i solve twice the square of a positive integer is 35 more than 9 times that integer?
\n" ); document.write( "what will the integer be? will it be 7 \n" ); document.write( "

Algebra.Com's Answer #52330 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
First, see if you can write an equation from the given information.
\n" ); document.write( "Let the positive integer be called n.
\n" ); document.write( "1) Twice the square of a positive integer...write this as $\"2n%5E2\"$
\n" ); document.write( "...is (=) 35 more than 9 times the integer...write this as $\"9n%2B35\"$
\n" ); document.write( "Now put it alltogether to get:
\n" ); document.write( " $\"2n%5E2+=+9n%2B35\"$ Now rearrange this into a quadratic equation so it can be solved:
\n" ); document.write( " $\"2n%5E2+-+9n+-+35+=+0\"$ This quadratic equation can be factored.
\n" ); document.write( " $\"%282n%2B5%29%28n-7%29+=+0\"$ Now apply the zero product principle.
\n" ); document.write( " $\"2n%2B5+=+0\"$ and/or $\"n-7+=+0\"$
\n" ); document.write( "If $\"2n%2B5+=+0\"$ then $\"2n+=+-5\"$ so $\"n+=+-5%2F2\"$ Discard this solution as you want only the positive solution.
\n" ); document.write( " $\"n-7+=+0\"$ so $\"n+=+7\"$ This is the solution you want.
\n" ); document.write( "The positive integer is 7
\n" ); document.write( "Check:
\n" ); document.write( "Twice the square of a positive integer...this is $\"2%287%29%5E2+=+2%2849%29\"$ = 98
\n" ); document.write( "...is (=) 35 more than 9 times the integer... this is $\"9%2A%287%29%2B35+=+63%2B35\"$ = 98
\n" ); document.write( "Neat, huh? \n" ); document.write( "

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