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

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.