To find the answer to "What two numbers have a product of 165 and a sum of -75?" we first state what we know. We are looking for x and y and we know that x • y = 165 and x + y = -75.
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 = -75 and solve it for y to get y = -75 - x. Then, we replace y in x • y = 165 with -75 - x to get this:
x • (-75 - x) = 165
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 165 and a sum of -75. The numbers are:
-72.73138
-2.26862
That's it! The two numbers that have a product of 165 and a sum of -75 are -72.73138 and -2.26862 as proven below:
-72.73138 • -2.26862 ≈ 165
-72.73138 + -2.26862 = -75
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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