*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 "="*

*n*^{2}* (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, *n*^{2}* = 54 + 3n OR n*^{2}* = 3n + 54 -- now we need to solve the equation to find the value of n.*

* -3n -3n*

* * *n*^{2}* - 3n = 54*

* -54 -54*

*n*^{2}* - 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.__