To find the answer to "What two numbers have a product of -17 and a sum of -111?" we first state what we know. We are looking for x and y and we know that x • y = -17 and x + y = -111.
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 = -111 and solve it for y to get y = -111 - x. Then, we replace y in x • y = -17 with -111 - x to get this:
x • (-111 - x) = -17
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 -17 and a sum of -111. The numbers are:
-111.15294
0.15294
That's it! The two numbers that have a product of -17 and a sum of -111 are -111.15294 and 0.15294 as proven below:
-111.15294 • 0.15294 ≈ -17
-111.15294 + 0.15294 = -111
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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