SOLUTION: Find all solutions to the equation: x - 10 sqrt(x) + 25 = 0 I figured out via guess and check that x = 25 but how do i solve for it using algebra? also is there more then one

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Question 683434: Find all solutions to the equation:
x - 10 sqrt(x) + 25 = 0
I figured out via guess and check that x = 25 but how do i solve for it using algebra? also is there more then one answer?
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
use the theorem


%28x-y%29%5E2=x%5E2-2xy%2By%5E2


x-10sqrt%28x%29+%2B+25+=+0+...in your case x is actually sqrt%28x%29, and y is 5
so, you have:
%28sqrt%28x%29-5%29%5E2+=+0+
this will be equal to zero if sqrt%28x%29-5+=+0+
so, we have
sqrt%28x%29=+5+....raise both sides to the power of two
%28sqrt%28x%29%29%5E2=+5%5E2+
x=+25+

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

x - 10 sqrt(x) + 25 = 0
I figured out via guess and check that x = 25 but how do i solve for it using algebra? also is there more then one answer?

x+-+10sqrt%28x%29+%2B+25+=+0

x+%2B+25+=+10sqrt%28x%29 ------ Adding 10sqrt%28x%29

%28x+%2B+25%29%5E2+=+%2810sqrt%28x%29%29%5E2 ------ Squaring both sides

x%5E2+%2B+50x+%2B+625+=+100x

x%5E2+%2B+50x+-+100x+%2B+625+=+0

x%5E2+-+50x+%2B+625+=+0

(x - 25)(x - 25) = 0

highlight_green%28x+=+25%29

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