Final answer:
To find the two numbers whose sum is 25 and product is -2394, we can set up a system of equations and solve them to get the pairs (54, -29) and (-29, 54).
Step-by-step explanation:
We are looking to find two numbers whose sum is 25 and whose product is -2394. Let's denote these two numbers as x and y.
The equations based on the given conditions are:
- x + y = 25
- x * y = -2394
First, solve the first equation for y:
y = 25 - x
Next, substitute this into the second equation:
x * (25 - x) = -2394
Now, expand and simplify:
25x - x^2 = -2394
Bring all terms to one side to solve for x:
x^2 - 25x - 2394 = 0
This is a quadratic equation, which we can factor or use the quadratic formula to solve. After factoring, we find that the two possible pairs for x and y are (54, -29) and (-29, 54).