Solve the equation for \( x \). (Round your answer to three decimal places.) \[ \arctan (2 x-9)=-1 \]

To solve the equation \( \arctan(2x - 9) = -1 \), we start by taking the tangent on both sides to eliminate the arctangent: \[ 2x - 9 = \tan(-1) \] We know that \( \tan(-1) \) is equal to \(-\tan(1)\). The value of \(\tan(1)\) is approximately \(1.5574\), thus: \[ \tan(-1) \approx -1.5574 \] Plugging that into our equation gives: \[ 2x - 9 = -1.5574 \] Now, we solve for \(x\): \[ 2x = -1.5574 + 9 \] \[ 2x = 7.4426 \] \[ x = \frac{7.4426}{2} \] \[ x \approx 3.7213 \] Rounding this to three decimal places, we get: \[ \boxed{3.721} \]