What two numbers have a product of 60 and a sum of -137?




To find the answer to "What two numbers have a product of 60 and a sum of -137?" we first state what we know. We are looking for x and y and we know that x • y = 60 and x + y = -137.

Before we keep going, it is important to know that x • y is the same as y • x and x + y is the same as y + x. The two variables are interchangeable. Which means that when we create one equation to solve the problem, we will have two answers.


To solve the problem, we take x + y = -137 and solve it for y to get y = -137 - x. Then, we replace y in x • y = 60 with -137 - x to get this:

x • (-137 - x) = 60

Like we said above, the x and y are interchangeable, therefore the x in the equation above could also be y. The bottom line is that when we solved the equation we got two answers which are the two numbers that have a product of 60 and a sum of -137. The numbers are:

-136.56063
-0.43937


That's it! The two numbers that have a product of 60 and a sum of -137 are -136.56063 and -0.43937 as proven below:

-136.56063 • -0.43937 ≈ 60

-136.56063 + -0.43937 = -137

Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.

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