To find the answer to "What two numbers have a product of 140 and a sum of -34?" we first state what we know. We are looking for x and y and we know that x • y = 140 and x + y = -34.
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 = -34 and solve it for y to get y = -34 - x. Then, we replace y in x • y = 140 with -34 - x to get this:
x • (-34 - x) = 140
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 140 and a sum of -34. The numbers are:
-29.20656
-4.79344
That's it! The two numbers that have a product of 140 and a sum of -34 are -29.20656 and -4.79344 as proven below:
-29.20656 • -4.79344 ≈ 140
-29.20656 + -4.79344 = -34
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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