To find the answer to "What two numbers have a product of 153 and a sum of -42?" we first state what we know. We are looking for x and y and we know that x • y = 153 and x + y = -42.
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 = -42 and solve it for y to get y = -42 - x. Then, we replace y in x • y = 153 with -42 - x to get this:
x • (-42 - x) = 153
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 153 and a sum of -42. The numbers are:
-37.97056
-4.02944
That's it! The two numbers that have a product of 153 and a sum of -42 are -37.97056 and -4.02944 as proven below:
-37.97056 • -4.02944 ≈ 153
-37.97056 + -4.02944 = -42
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
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