Question

6 times a number is 27 less than the square of that number. Find the positive solution.

Answer 1

Let x = your number.

6x = x^2 - 27. Subtract 6x from each side.

0 = x^2 - 6x - 27. Factor

0 = (x-9) (x+3). Set each term equal to zero

(x+3) = 0. Subtract 3 from each side.

x = -3. This is the negative solution.

(x-9) = 0. Add 9 to each side.

x = 9. This is the positive solution.

Answer 2

The positive solution will be "x = 3, -9". To understand the calculation check below.

Factorization

According to the question,

Let,

The number be "x".

6x = x² - 27

Now,

          x² - 6x - 27 = 0

By applying factorization, we get

→ x² - 3x + 9x - 27 = 0

By taking common,

x (x - 3) + 9 (x - 3) = 0

        (x + 9) (x - 3) = 0

                  (x + 9) = 0

                          x = -9

or,

                   (x - 3) = 0

                          x = 3

Thus the answer above is correct.

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