Answer:
The correct equation to solve for "x" is:
[tex]x^2+8x-308=0[/tex]
(first option in your list)
Step-by-step explanation:
Let's say that since the integers in question are separated on the number line, we can call them x, and y with for example y being the larger one (two the right of x on the number line). Since the two integers are 8 units apart, then we can write in mathematical form:
y - x = 8 (because y is the larger of the two numbers)
and solving for "y" we get:
y = x + 8
we also know that their product is 308, which we can write in the following form:
x * y = 308
Now, replacing y by "x + 8", we get:
[tex]x*y=308\\x\,(x+8)=308\\x^2+8x=308\\x^2+8x-308=0[/tex]
Therefore, the correct equation is the first one listed among your answer options.
