To find the answer to "What two numbers have a product of 127 and a sum of -138?" we first state what we know. We are looking for x and y and we know that x • y = 127 and x + y = -138.
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 = -138 and solve it for y to get y = -138 - x. Then, we replace y in x • y = 127 with -138 - x to get this:
x • (-138 - x) = 127
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 127 and a sum of -138. The numbers are:
-137.07349
-0.92651
That's it! The two numbers that have a product of 127 and a sum of -138 are -137.07349 and -0.92651 as proven below:
-137.07349 • -0.92651 ≈ 127
-137.07349 + -0.92651 = -138
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
Product Sum Calculator
Need the answer to a similar problem? Submit another product and sum below to find the two numbers that make your product and sum.