To find the answer to "What two numbers have a product of 157 and a sum of -187?" we first state what we know. We are looking for x and y and we know that x • y = 157 and x + y = -187.
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 = -187 and solve it for y to get y = -187 - x. Then, we replace y in x • y = 157 with -187 - x to get this:
x • (-187 - x) = 157
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 157 and a sum of -187. The numbers are:
-186.15662
-0.84338
That's it! The two numbers that have a product of 157 and a sum of -187 are -186.15662 and -0.84338 as proven below:
-186.15662 • -0.84338 ≈ 157
-186.15662 + -0.84338 = -187
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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