SOLUTION: if 6 is added to a number and then subtracted from the same number, the product of the sum and the difference is 189. What is the number?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: if 6 is added to a number and then subtracted from the same number, the product of the sum and the difference is 189. What is the number?       Log On


   

Question 211397: if 6 is added to a number and then subtracted from the same number, the product of the sum and the difference is 189. What is the number?
Found 2 solutions by rapaljer, Alan3354:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the number
x+6 = the "sum"
x-6 = the "difference"

The equation is:
(x+6)(x-6) = 189
x^2 -36 = 189

Since this is quadratic, set it equal to zero:
x^2 -36-189=0
x^2-225=0

There are two ways to solve this. You can factor it:
(x-15)(x+15) = 0
x=15 or x=-15

Or you can use the square root method:
x^2 -225 =0
x^2=225
x=+sqrt%28225%29 or x=+-sqrt%28225%29
x+=+15 or x=-15

R^2

Dr. Robert J. Rapalje, Retired
Seminole Community College

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
if 6 is added to a number and then subtracted from the same number, the product of the sum and the difference is 189. What is the number?
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The quick and easy way:
189 + 6^2 = 225
225 is the square of the original number - sqrt(225) = ±15
9*21 = 189
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The hard way:
(n-6)*(n+6) = 189
n^2 - 36 = 189
n^2 = 225
n = 15 (and -15)
Not much difference in the 2 methods