Question

Solve the following word problem by using an equation and factoring. The sum of a positive number and its square is 20. What is the number?
A. 1
B. 2
C. 3
D. 4
E. 5

Answer 1

Number:  n
square of number:  n^2
sum of n and n^2 is n+n^2=20
Rewriting this equation, we get n^2+n-20=0 = (n+5)(n-4) = 0

Then n+5=0 and n-4=0, so n = -5 and n = 4.

You must check both results.  It could happen that both are correct, or that only one is correct.