Question

If 3 is added to twice the square of an integer, the result is equal to seven times the integer. Find the integer

Answer 1

`(1)/(2)` and
`3`

Explanation:

We will set up an equation based on the problem using
`x` to represent the integer.

`3+2x^2 = 7x`

Now, we will solve for
`x` by setting the equation equal to 0 and factoring.

`2x^2 -7x + 3 =0\\2x^2 - 6x - x +3 =0\\2x(x-3) -1(x-3)=0\\(2x-1)(x-3) =0\\x=(1)/(2), 3`

So, the integer can be either
`(1)/(2)` or
`3`.