SOLUTION: Solve for x, √x + √{x - √(1-x} = 1

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Question 1206802: Solve for x,
√x + √{x - √(1-x} = 1
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solve for+x,

sqrt%28x%29+%2B+sqrt%28x+-+sqrt%281-x%29%29+=+1
+sqrt%28x+-+sqrt%281-x%29%29+=+1-sqrt%28x%29+...square both sides
%28sqrt%28x+-+sqrt%281-x%29%29%29%5E2+=%28+1-sqrt%28x%29%29%5E2+
x+-+sqrt%281-x%29+=+1-2sqrt%28x%29%2Bx...simplify
-+sqrt%281-x%29+=+1-2sqrt%28x%29...square both sides
%28-+sqrt%281-x%29%29%5E2+=+%281-2sqrt%28x%29%29%5E2
1-x+=1+-+4sqrt%28x%29+%2B4x
4sqrt%28x%29=1+-+1+%2B4x%2Bx
4sqrt%28x%29=5x...square both sides
16x=25x%5E2..simplify
16=25x
x=16%2F25