Final answer:
To find the two numbers, we can set up an equation using the given information and solve for the variables. By factoring the quadratic equation, we find that the two numbers are -15 and -7, or 7 and 15.
Step-by-step explanation:
Let x be one number and x + 8 be the other number.
We know that the product of the numbers is 105. So, we can write the equation:
x * (x + 8) = 105
Expanding the equation, we get:
x^2 + 8x = 105
Subtracting 105 from both sides, we have:
x^2 + 8x - 105 = 0
Now, we can solve this quadratic equation by factoring or by using the quadratic formula. Factoring, we get:
(x + 15)(x - 7) = 0
Setting each factor equal to zero, we find the solutions:
x + 15 = 0 or x - 7 = 0
x = -15 or x = 7
So, the two numbers are -15 and -7, or 7 and 15.