To find the answer to "What two numbers have a product of 133 and a sum of -61?" we first state what we know. We are looking for x and y and we know that x • y = 133 and x + y = -61.
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 = -61 and solve it for y to get y = -61 - x. Then, we replace y in x • y = 133 with -61 - x to get this:
x • (-61 - x) = 133
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 133 and a sum of -61. The numbers are:
-58.73562
-2.26438
That's it! The two numbers that have a product of 133 and a sum of -61 are -58.73562 and -2.26438 as proven below:
-58.73562 • -2.26438 ≈ 133
-58.73562 + -2.26438 = -61
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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