SOLUTION: In 10 years from now, my age will be the square of my age 10 years ago. How old am I?

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Question 1147629: In 10 years from now, my age will be the square of my age 10 years ago. How old am I?
Found 3 solutions by josgarithmetic, VFBundy, ikleyn:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
x%2B10=%28x-10%29%5E2
x%2B10=x%5E2-20x%2B100
x=x%5E2-20x%2B90
x%5E2-21x%2B90=0


2*45=2*5*3*3=15*6
%28x-6%29%28x-15%29=0

highlight%28x=15%29
Because x=6 will not work.
Age ten years ago must be non-negative.

Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
n + 10 = (n - 10)²

n + 10 = n² - 20n + 100

n² - 21n + 90 = 0

(n - 15)(n - 6) = 0

n = 15 and n = 6

You could be either 6 or 15.

Check it:
6 + 10 = (6 - 10)² [CHECKS]
15 + 10 = (15 - 10)² [CHECKS]

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

Your equation is


    a + 10 = (a-10)^2


Simplify and solve


    a + 10 = a^2 - 20a + 100


    a^2 - 21a + 90 = 0


    (a-15)*(a-6) = 0.


Of the two roots, only "15" allows to subtract 10 and obtain the positive age ten years ago.


Hence, the problem has a unique ANSWER.  Your age is 15 years.