To find the answer to "What two numbers have a product of 199 and a sum of -112?" we first state what we know. We are looking for x and y and we know that x • y = 199 and x + y = -112.
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 = -112 and solve it for y to get y = -112 - x. Then, we replace y in x • y = 199 with -112 - x to get this:
x • (-112 - x) = 199
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 199 and a sum of -112. The numbers are:
-110.1941
-1.8059
That's it! The two numbers that have a product of 199 and a sum of -112 are -110.1941 and -1.8059 as proven below:
-110.1941 • -1.8059 ≈ 199
-110.1941 + -1.8059 = -112
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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