To find the answer to "What two numbers have a product of -123 and a sum of -140?" we first state what we know. We are looking for x and y and we know that x • y = -123 and x + y = -140.
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 = -140 and solve it for y to get y = -140 - x. Then, we replace y in x • y = -123 with -140 - x to get this:
x • (-140 - x) = -123
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 -123 and a sum of -140. The numbers are:
-140.87313
0.87313
That's it! The two numbers that have a product of -123 and a sum of -140 are -140.87313 and 0.87313 as proven below:
-140.87313 • 0.87313 ≈ -123
-140.87313 + 0.87313 = -140
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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