Question 582720
{{{ x - sqrt(10) = 1 - sqrt(x) }}}
Add {{{ sqrt(x) }}} to both sides
Add {{{ sqrt(10) }}}  to both sides
{{{ x + sqrt(x) = sqrt(10) + 1 }}}
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Let {{{ x = z^2 }}}
{{{ z^2 + z = sqrt(10) + 1 }}}
Complete the square
{{{ z^2 + z + (1/2)^2 = sqrt(10) + 1 + (1/2)^2 }}}
{{{ z^2 + z + 1/4 = sqrt(10) + 1 + 1/4 }}}
{{{ ( z + 1/2)^2 = sqrt(10) + 5/4 }}}
Take the square root of both sides
{{{ z + 1/2 = sqrt( sqrt(10) + 5/4 ) }}}
{{{ sqrt(x) + 1/2 = sqrt( sqrt(10) + 5/4 ) }}}
{{{ sqrt(x)  = sqrt( sqrt(10) + 5/4  ) - 1/2 }}}
Square both sides
{{{ x = sqrt(10) + 5/4 - sqrt( sqrt(10) + 5/4) + 1/4 }}}
{{{ x = sqrt(10)  -  sqrt( sqrt(10) + 5/4) + 3/2 }}}
This looks pretty strange. You might want
a 2nd opinion