The square of a negative number is fifty-four more than three times the negative number. Find the number.

Question

The square of a negative number is fifty-four more than three times the negative number. Find the number.

Answer 1

Let x be the negative number. The square of a negative number (x²) is (=) fifty-four more (54 +) than three times the negative number (3x):

x² = 54 + 3x

x² - 3x - 54 = 0

Solve for x by factoring. You'll get two answers, one positive and one negative. Since x is a negative numbers, the negative answer is the correct one.

Answer 2

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.

-3n -3n

n² - 3n = 54

-54 -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.