To find the answer to "What two numbers have a product of -120 and a sum of 192?" we first state what we know. We are looking for x and y and we know that x • y = -120 and x + y = 192.
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 = 192 and solve it for y to get y = 192 - x. Then, we replace y in x • y = -120 with 192 - x to get this:
x • (192 - x) = -120
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 -120 and a sum of 192. The numbers are:
-0.62298
192.62298
That's it! The two numbers that have a product of -120 and a sum of 192 are -0.62298 and 192.62298 as proven below:
-0.62298 • 192.62298 ≈ -120
-0.62298 + 192.62298 = 192
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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