The sum of two numbers is 30, their product is 176. What are the two numbers

We have two numbers "x" and "y",

we suggest this system of equations.

x+y=30

xy=176

Solve by substitution method.

x=30-y

(30-y) y=176

30y-y²=176

y²-30y+176=0

We solve this square equation:

y=[30⁺₋√ (900-4*176) ] / 2 = (30⁺₋14) / 2

two solutions:

y₁ = (30-14) / 2=8 ⇒x=30-y ⇒ x=30-8=22

y₂ = (30+14) / 2=22 ⇒x=30-y ⇒x=30-22=8

Therefore: the numbers are 8 and 22

To check:

the sum of two numbers 8+22 is 30

their product 8*22 is 176

8,22 those are the two numbers 8+22=30

8x22=176