To find the answer to "What two numbers have a product of 54 and a sum of -40?" we first state what we know. We are looking for x and y and we know that x • y = 54 and x + y = -40.
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 = -40 and solve it for y to get y = -40 - x. Then, we replace y in x • y = 54 with -40 - x to get this:
x • (-40 - x) = 54
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 54 and a sum of -40. The numbers are:
-38.60108
-1.39892
That's it! The two numbers that have a product of 54 and a sum of -40 are -38.60108 and -1.39892 as proven below:
-38.60108 • -1.39892 ≈ 54
-38.60108 + -1.39892 = -40
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.