To find the answer to "What two numbers have a product of 144 and a sum of -89?" we first state what we know. We are looking for x and y and we know that x • y = 144 and x + y = -89.
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 = -89 and solve it for y to get y = -89 - x. Then, we replace y in x • y = 144 with -89 - x to get this:
x • (-89 - x) = 144
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 144 and a sum of -89. The numbers are:
-87.35149
-1.64851
That's it! The two numbers that have a product of 144 and a sum of -89 are -87.35149 and -1.64851 as proven below:
-87.35149 • -1.64851 ≈ 144
-87.35149 + -1.64851 = -89
Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.
Product Sum Calculator
Need the answer to a similar problem? Submit another product and sum below to find the two numbers that make your product and sum.