To find the answer to "What two numbers have a product of 38 and a sum of 45?" we first state what we know. We are looking for x and y and we know that x • y = 38 and x + y = 45.
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 = 45 and solve it for y to get y = 45 - x. Then, we replace y in x • y = 38 with 45 - x to get this:
x • (45 - x) = 38
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 38 and a sum of 45. The numbers are:
0.86091
44.13909
That's it! The two numbers that have a product of 38 and a sum of 45 are 0.86091 and 44.13909 as proven below:
0.86091 • 44.13909 ≈ 38
0.86091 + 44.13909 = 45
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.