What two numbers when multiplied equal -264 and also can add up to 25?

Answer 1

-239

Answer 2

Since the product of two numbers is -264, we express this as:

xy = -264

Since the sum of two numbers is 25, we express this as:

x + y = 25

These are the equations we have based on the problem:

xy = -264

x + y = 25

There are some methods to work out this problem.

1. Use elimination or substitution method. This method deals with computation by hands.
2. Solve for either x or y. Then, graph the functions and determine their intersection points.

I select the first method to work out this problem.

xy = -264

Solve for x to get.

y = -264/x

Substitute that for the second equation to get:

x - 264/x = 25

Solve for x by rearranging the terms.

(x - 264/x = 25)x

x² - 264 = 25x

x² - 25x - 264 = 0

(x - 33)(x + 8) = 0

So we have x = 33 and x = -8.

Substitute either of these x values, and we have similar y values, which are y = -33 and y = 8. The pattern of the solutions to this problem is: No matter what two numbers you have found for a certain variable of the function, the values of another variable should be similar to the one you have found.

Check each solution:

x = 33 and y = -8 gives:

33(-8) = -264

33 + (-8) = 25

So x = 33 and y = -8 works.

If we try x = -33 and y = 8, then the solution doesn't work since -33 + 8 = -25, not 25.