SOLUTION: Please help me solve this equation:{{{sqrt(x)-sqrt(x-2)-1=0}}}

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Question 965230: Please help me solve this equation:sqrt%28x%29-sqrt%28x-2%29-1=0
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve this equation:sqrt%28x%29-sqrt%28x-2%29-1=0
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sqrt%28x%29=+sqrt%28x-2%29-1
Square both sides
x+=+%28x-2%29+-+2sqrt%28x-2%29+%2B+1
1+=+-2sqrt%28x-2%29
Square again.
etc

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+sqrt%28x%29+-+sqrt%28+x-2+%29+-+1+=+0+
+sqrt%28x%29+=+sqrt%28+x-2+%29+%2B+1+
Square both sides
+x+=+%28+sqrt%28+x-2+%29+%2B+1+%29%5E2+
+x+=+x-2+%2B+2%2Asqrt%28+x-2+%29+%2B+1+
subtract +x+ from both sides
+0+=+-2+%2B+2%2Asqrt%28+x-2+%29+%2B+1+
+2%2Asqrt%28+x-2+%29+=+1+
+sqrt%28+x-2+%29+=+1%2F2+
Square both sides
+x+-+2+=+1%2F4+
+x+=+8%2F4+%2B+1%2F4+
+x+=+9%2F4+
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check:
+sqrt%28x%29+-+sqrt%28+x-2+%29+-+1+=+0+
+sqrt%28+9%2F4+%29+-+sqrt%28+9%2F4+-+2+%29+-+1+=+0+
+3%2F2+-+sqrt%28+9%2F4+-+8%2F4+%29+-+1+=+0+
+3%2F2+-+sqrt%28+1%2F4+%29+-+1+=+0+
+3%2F2+-+1%2F2+-+2%2F2+=+0+
+3%2F2+-+3%2F2+=+0+
+0+=+0+
OK