To find the answer to "What two numbers have a product of 192 and a sum of -100?" we first state what we know. We are looking for x and y and we know that x • y = 192 and x + y = -100.
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 = -100 and solve it for y to get y = -100 - x. Then, we replace y in x • y = 192 with -100 - x to get this:
x • (-100 - x) = 192
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 192 and a sum of -100. The numbers are:
-98.04165
-1.95835
That's it! The two numbers that have a product of 192 and a sum of -100 are -98.04165 and -1.95835 as proven below:
-98.04165 • -1.95835 ≈ 192
-98.04165 + -1.95835 = -100
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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