The square of a negative number is twenty-eight more than three times the negative number. Find the number.

-4 that's the end result

The number is x

it is negative

the square is 28 more than 3 times itself

x²=28+3x

minus (28+3x)

x²-3x-28=0

factor

(x-7) (x+4) = 0

set to zero

x-7=0

x=7

this is not the answer because we were told the number was negative

x+4=0

x=-4

correct

the number is - 4

test

(-4) ²=28+3 (-4)

16=28-12

16=16

check

the number is - 4