SOLUTION: If three is added to twice the square of an integer, the result is equal to seven times the integer. Find the integer.

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.
Found 2 solutions by DrBeeee, ben720:
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let n = the integer
The problem statement gives us
(1) 3 + 2*n^2 = 7*n or
(2) 2*n^2 - 7*n + 3 = 0 which factors to
(3) (2n - 1)*(n - 3) = 0
Set each factor equal to zero and solve for n gives us
(4) n = 1/2,3
Since n is an integer we select
(5) n = 3
Check this with (1).
Is (3 + 2*3^2 = 7*3)?
Is (3 + 2*9 = 21)?
Is (3 + 18 = 21)?
Is (21 = 21)? Yes
Answer: The integer is 3.

Answer by ben720(159) (Show Source): You can put this solution on YOUR website!
If three is added to twice the square of x, its 7x

Subtract 7x from both sides

Use the quadratic formula:

Substitute a, b, c

Multiply

+-sqrt(25) is 5 or -5. First, we'll do +5

OR

X = 3 or 2
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