SOLUTION: solve the following equation: {{{ x-1= sqrt(x+5 ) }}}

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Question 1011047: solve the following equation:
+x-1=+sqrt%28x%2B5+%29+
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
By looking at the right side:
+x+%3E=+-5+ otherwise, the right side is
imaginary and the left side is a negative number
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But also, unless +x+%3E=+1+ the left side is negative
and the right side is positive. This restriction takes
precedence over the other restriction
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Square both sides
+x-1=+sqrt%28x%2B5+%29+
+%28+x+-+1+%29%5E2+=+x+%2B+5+
+x%5E2+-+2x+%2B+1+=+x+%2B+5+
+x%5E2+-+3x+-+4+=+0+
+%28+x+-+4+%29%2A%28+x+%2B+1+%29+=+0+
+x+=+4+
+x+=+-1+
( this value doesn't work unless the right side is +-sqrt%28+x%2B5+%29+ )
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+x-1=+sqrt%28x%2B5+%29+
+4-1=+sqrt%284%2B5+%29+
+3+=+sqrt%289%29+
+3+=+3+
So, +x=4+ is the answer