SOLUTION: Could someone please help me solve this equation? {{{ sqrt(x) - sqrt(x-45) = 3 }}} Thank you for your help!!

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Question 709801: Could someone please help me solve this equation?
+sqrt%28x%29+-+sqrt%28x-45%29+=+3+
Thank you for your help!!
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(x) - sqrt(x-45) = 3
----
Square both sides to get:
----
x - 2sqrt(x^2-45x) + x-45 = 9
---
Simplify:
2sqrt(x^2-45x) = 54-2x
----
sqrt(x^2-45x) = 27-x
----
Square both sides:
x^2-45x = 729-54x+x^2
----
9x = 729
x = 81
=============
Cheers,
Stan H.
==============

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
+sqrt%28x%29+-+sqrt%28x-45%29+=+3+.....square both sides

+%28sqrt%28x%29+-+sqrt%28x-45%29%29%5E2+=+3%5E2+

+%28sqrt%28x%29%29%5E2+-+2sqrt%28x%29%2Asqrt%28x-45%29%2B%28sqrt%28x-45%29%29%5E2+=+9+

+x+-+2sqrt%28x%29%2Asqrt%28x-45%29%2B%28x-45%29+=+9+

+x+-+2sqrt%28x%28x-45%29%29%2Bx-45+=+9+

+2x+-+2sqrt%28x%28x-45%29%29+=+9%2B45+

++-+2sqrt%28x%28x-45%29%29+=-2x%2B54+

++sqrt%28x%28x-45%29%29+=-2x%2F-2%2B54%2F-2+

++sqrt%28x%28x-45%29%29+=x-27+

++%28sqrt%28x%28x-45%29%29%29%5E2+=%28x-27%29%5E2+...........square both sides

++x%28x-45%29+=x%5E2-54x%2B729+

++x%5E2-45x+=x%5E2-54x%2B729+

++cross%28x%5E2%29-45x+=cross%28x%5E2%29-54x%2B729+

++-45x+=-54x%2B729+

++-45x%2B54x+=729+

+9x+=729+

+x+=729%2F8+

+highlight%28x+=81%29+

check:
+sqrt%28x%29+-+sqrt%28x-45%29+=+3+....plug in +highlight%28x+=81%29+

+sqrt%2881%29+-+sqrt%2881-45%29+=+3+
+9+-+sqrt%2836%29+=+3+
+9+-+6+=+3+
+3+=+3+