To find the answer to "What two numbers have a product of 127 and a sum of -80?" we first state what we know. We are looking for x and y and we know that x • y = 127 and x + y = -80.
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 = -80 and solve it for y to get y = -80 - x. Then, we replace y in x • y = 127 with -80 - x to get this:
x • (-80 - 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 -80. The numbers are:
-78.37968
-1.62032
That's it! The two numbers that have a product of 127 and a sum of -80 are -78.37968 and -1.62032 as proven below:
-78.37968 • -1.62032 ≈ 127
-78.37968 + -1.62032 = -80
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.