To find the answer to "What two numbers have a product of -7 and a sum of 4?" we first state what we know. We are looking for x and y and we know that x • y = -7 and x + y = 4.
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 = 4 and solve it for y to get y = 4 - x. Then, we replace y in x • y = -7 with 4 - x to get this:
x • (4 - x) = -7
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 -7 and a sum of 4. The numbers are:
-1.31662
5.31662
That's it! The two numbers that have a product of -7 and a sum of 4 are -1.31662 and 5.31662 as proven below:
-1.31662 • 5.31662 ≈ -7
-1.31662 + 5.31662 = 4
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.