First and foremost, let's assign our variable. We will let "n" represent our unknown number.
"THE SQUARE OF A NEGATIVE NUMBER": this phrase tells us that our variable (n) will be squared.
"IS": this word tell us that this is where the "=" goes.
"FIFTY FOUR MORE THAN": this phrase tells us that we are adding 54 to something on the right side of the equal sign.
"THREE TIMES THE NEGATIVE NUMBER": put simply, on the right side of the equal sign we will be multiplying our variable (n) by 3.
ON THE LEFT SIDE TO THE "="
n2 (THE SQUARE OF A NEGATIVE NUMBER)
ON THE RIGHT SIDE OF THE "="
We know we are adding 54 to something (FIFTY FOUR MORE THAN)
That something, we now know, is 3 times n (THREE TIMES THE NEGATIVE NUMBER)
So, n2 = 54 + 3n OR n2 = 3n + 54 -- now we need to solve the equation to find the value of n.
n2 - 3n = 54
n2 - 3n - 54 = 0
(n - 9)(n +6) =0
Now, after factoring the quadratic, we see that there are 2 possible solutions, but what did the question specifically say about our number?.... That it is NEGATIVE!!
So, our answer will be: n = -6.