To find the answer to "What two numbers have a product of 128 and a sum of -52?" we first state what we know. We are looking for x and y and we know that x • y = 128 and x + y = -52.
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 = -52 and solve it for y to get y = -52 - x. Then, we replace y in x • y = 128 with -52 - x to get this:
x • (-52 - x) = 128
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 128 and a sum of -52. The numbers are:
-49.4094
-2.5906
That's it! The two numbers that have a product of 128 and a sum of -52 are -49.4094 and -2.5906 as proven below:
-49.4094 • -2.5906 ≈ 128
-49.4094 + -2.5906 = -52
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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