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10 December, 04:22

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

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Answers (2)
  1. 10 December, 04:38
    0
    - 14 or 13

    Step-by-step 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
  2. 10 December, 05:56
    0
    -14 or 13

    Step-by-step 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
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