Solve `x gt sqrt(1-x)`

Explanation

Given inequality can be solved by squaring both sides.
But sometimes squaring gives extraneous solutions which do not satisfy the original inequality. Before squaring we must restrict x for which terms in the given inequality are well defined.
`x gt sqrt((1-x))`. Here x must be positive.
Now, `sqrt(1-x)` is defined only when `1-x ge 0 " or " x le 1`
Thus `0 le x le 1 " " ` (1)
Squaring given inequality both sides, `x^(2) gt 1 -x`
` implies x^(2) +x-1 gt 0`
`implies (x-(-1-sqrt(5))/(2))(x-(-1+sqrt(5))/(2)) gt 0`

`implies x lt (-1-sqrt(5))/(2) " or "x gt (-1+sqrt(5))/(2) " " ` (2)
From (1) and (2), `x in ((sqrt(5)-1)/(2),1]`