Question

If the sum of a number and its square is 182, what is the number ?

Answer 1

- 14 or 13

Explanation:

let the number be n then it's square is n² and

n² + n = 182 ( subtract 182 from both sides )

n² + n - 182 = 0 ← in standard form

(n + 14)(n - 13) = 0 ← in factored form

Equate each factor to zero and solve for n

n + 14 = 0 ⇒ n = - 14

n - 13 = 0 ⇒ n = 13

As a check

(-14)² - 14 = 196 - 14 = 182

13² + 13 = 169 + 13 = 182

Answer 2

-14 or 13

Explanation:

x + x^2 = 182

x^2 + x - 182 = 0

rearrange and solve by completing the square

x^2 + x = 182

x^2 + x + 1/4 = 182.25

(x + 1/2)(x + 1/2) = 182.25

(x + 1/2)^2 = 182.25

x + 1/2 = root 182.25

x = + or - root 182.25 - 0.5

x = + or - 13.5 - 0.5

x = 13 or x = - 14