To find the answer to "What two numbers have a product of 169 and a sum of -29?" we first state what we know. We are looking for x and y and we know that x • y = 169 and x + y = -29.
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 = -29 and solve it for y to get y = -29 - x. Then, we replace y in x • y = 169 with -29 - x to get this:
x • (-29 - x) = 169
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 169 and a sum of -29. The numbers are:
-20.92262
-8.07738
That's it! The two numbers that have a product of 169 and a sum of -29 are -20.92262 and -8.07738 as proven below:
-20.92262 • -8.07738 ≈ 169
-20.92262 + -8.07738 = -29
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.