Geometric Nightmare

Geometry Level 3

Diagram above shows a unit square \(ABCD\), the line \(AD\) is extended to point \(E\) such that \(BE\) is a straight line intersecting the line extended line of \(AD\) at \(E\) with \(F\) as a point of \(BF\) that is a point on line side \(CD\) such that \(FE = 1 \). Let distance \(DE \) be denoted as \(x\). Find the value of \(x\).

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