Question 73068
First, see if you can write an equation from the given information.
Let the positive integer be called n.
1) Twice the square of a positive integer...write this as {{{2n^2}}}
...is (=) 35 more than 9 times the integer...write this as {{{9n+35}}}
Now put it alltogether to get:
{{{2n^2 = 9n+35}}} Now rearrange this into a quadratic equation so it can be solved:
{{{2n^2 - 9n - 35 = 0}}} This quadratic equation can be factored.
{{{(2n+5)(n-7) = 0}}} Now apply the zero product principle.
{{{2n+5 = 0}}} and/or {{{n-7 = 0}}}
If {{{2n+5 = 0}}} then {{{2n = -5}}} so {{{n = -5/2}}} Discard this solution as you want only the positive solution.
{{{n-7 = 0}}} so {{{n = 7}}} This is the solution you want.
The positive integer is 7
Check:
Twice the square of a positive integer...this is {{{2(7)^2 = 2(49)}}} = 98
...is (=) 35 more than 9 times the integer... this is {{{9*(7)+35 = 63+35}}} = 98
Neat, huh?