SOLUTION: I am working on this in Applications and I can get to the last step but then I don't know how they get the answer: I have tried to multiply and add, subtract, and divide but I stil

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I am working on this in Applications and I can get to the last step but then I don't know how they get the answer: I have tried to multiply and add, subtract, and divide but I stil      Log On


   

Question 165868This question is from textbook Intermediate Algebra
: I am working on this in Applications and I can get to the last step but then I don't know how they get the answer: I have tried to multiply and add, subtract, and divide but I still can't understand the last step...
Here is and ex:
Find a negative real number such that the square of the sum of the number and 16 is equal to 36. (If there are two correct answers, either can be entered.)
I want to know how they get the number 256. this is how it is set up
x +16 squared =36
x squared + 32x+256=36
x squared + 32x = 220=0

I understand the steps except how they get the 256. Can you help me Please? This question is from textbook Intermediate Algebra

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number be -n (a negative real number), then, from the problem description, you have:
%28-n%2B16%29%5E2+=+36 "...the square of the sum of the number and 16 is equal to 36."
Square the left side of the equation.
n%5E2-32n%2B256+=+36 Subtract 36 from both sides.
n%5E2-32n%2B220+=+0 Solve by factoring this quadratic equation.
%28n-10%29%28n-22%29+=+0 So...
n+=+10 or n+=+22
The answers should be: -10 and -22