What two numbers have a product of 176 and a sum of -86?




To find the answer to "What two numbers have a product of 176 and a sum of -86?" we first state what we know. We are looking for x and y and we know that x • y = 176 and x + y = -86.

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 = -86 and solve it for y to get y = -86 - x. Then, we replace y in x • y = 176 with -86 - x to get this:

x • (-86 - x) = 176

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 176 and a sum of -86. The numbers are:

-83.90232
-2.09768


That's it! The two numbers that have a product of 176 and a sum of -86 are -83.90232 and -2.09768 as proven below:

-83.90232 • -2.09768 ≈ 176

-83.90232 + -2.09768 = -86

Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.

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