To find the answer to "What two numbers have a product of -27 and a sum of -24?" we first state what we know. We are looking for x and y and we know that x • y = -27 and x + y = -24.
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 = -24 and solve it for y to get y = -24 - x. Then, we replace y in x • y = -27 with -24 - x to get this:
x • (-24 - x) = -27
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 -27 and a sum of -24. The numbers are:
-25.0767
1.0767
That's it! The two numbers that have a product of -27 and a sum of -24 are -25.0767 and 1.0767 as proven below:
-25.0767 • 1.0767 ≈ -27
-25.0767 + 1.0767 = -24
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.