To find the answer to "What two numbers have a product of 173 and a sum of -51?" we first state what we know. We are looking for x and y and we know that x • y = 173 and x + y = -51.
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 = -51 and solve it for y to get y = -51 - x. Then, we replace y in x • y = 173 with -51 - x to get this:
x • (-51 - x) = 173
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 173 and a sum of -51. The numbers are:
-47.34605
-3.65395
That's it! The two numbers that have a product of 173 and a sum of -51 are -47.34605 and -3.65395 as proven below:
-47.34605 • -3.65395 ≈ 173
-47.34605 + -3.65395 = -51
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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