Question

The square of a negative number is 28 more than three times the negative number

Answer 1

Let the number be x, and remember that x is negative.

Then x^2 = 3x + 28.  Rearranging terms, x^2 - 3x - 28 = 0

Factoring, (x+4)(x-7) = 0.  Solving for x, x=-4 and x=7.  Discard x=7.

The answer is x=-4.

Check:  Is this true for x = -4?

"The square of a negative number is 28 more than three times the negative number."

(-4)^2 = 28 + 3(-4)             or    16 = 28 - 12                 yes, this is true.

Answer 2

Let x be the unknown negative number.

The square of the negative number: x2

is =

60 more than 4 times the negative number: 4x + 60

     x2 = 4x + 60

     x2 - 4x - 60 = 0

Factors to:

     (x-10)(x+6) = 0

     x = 10 and -6

Since the number is negative, x = -6

Check:

    x2 = 4x + 60

    (-6)2 = 4(-6)+60

    36 = -24 + 60

    36 = 36