3 times a number is 18 less than the square of that number. Find the negative solution.

Question

what is the negative solution for a quadratic function 

Answer 1

Hi Lura.

 

If you let N be the number, and then turn all of the words into math, we get

 

"3 times a number":  3*N

"is 18 less than the square of the number":   = N² - 18

 

Putting this all together, we get

 

3N = N² - 18

 

 

This is a quadratic, so to solve it we need to move everything to one side.

 

Subtract 3N from both sides:  0 = N² - 3N - 18

 

 

This factors:   0 = (N - 6)(N + 3)

 

Set each factor equal to zero:   N - 6 = 0    and    N + 3 = 0

 

Solving these we find that  N = 6  and  N = -3

 

They want the negative solution, so the answer is N = -3