To find the answer to "What two numbers have a product of 128 and a sum of -146?" we first state what we know. We are looking for x and y and we know that x • y = 128 and x + y = -146.
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 = -146 and solve it for y to get y = -146 - x. Then, we replace y in x • y = 128 with -146 - x to get this:
x • (-146 - 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 -146. The numbers are:
-145.11796
-0.88204
That's it! The two numbers that have a product of 128 and a sum of -146 are -145.11796 and -0.88204 as proven below:
-145.11796 • -0.88204 ≈ 128
-145.11796 + -0.88204 = -146
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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