To find the answer to "What two numbers have a product of -130 and a sum of -109?" we first state what we know. We are looking for x and y and we know that x • y = -130 and x + y = -109.
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 = -109 and solve it for y to get y = -109 - x. Then, we replace y in x • y = -130 with -109 - x to get this:
x • (-109 - x) = -130
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 -130 and a sum of -109. The numbers are:
-110.17989
1.17989
That's it! The two numbers that have a product of -130 and a sum of -109 are -110.17989 and 1.17989 as proven below:
-110.17989 • 1.17989 ≈ -130
-110.17989 + 1.17989 = -109
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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