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.
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
(
