The product of two numbers is 198 the sum of the numbers equals 29 find the two numbers

Define the two numbers:

Let one number be x and the other number be y.


Construct the two equations:

The product of the two numbers is 198:
xy = 198

The sum of the two numbers is 29:
x + y = 29


Solve for x and y:

xy = 198     (1)
x + y = 29 (2)


From equation (2):

x + y = 29
x = 29 - y 


Substitute x = 29-y into (1):

y(29 - y) = 198
29y - y² = 198
y² - 29y + 198 = 0
(y - 11)(y -18) = 0
y = 11 or y = 18


Substitute y = 11 into equation 2

x + y = 29
x + 11 = 29
x = 29 - 11
x = 18


The number are 11 and 18.