Matching exercise choose the correct one out of the alternatives $$A, B, C, D$$

Group $$-$$ $${\rm I}$$
$$P.$$ $${2^{nd}}$$ order differential equations
$$Q.$$ Non-linear algebraic equations
$$R.$$ Linear algebraic equations
$$S.$$ Numerical integration

Group $$-$$ $${\rm II}$$
$$(1)$$ Runge $$-$$ Kutta method
$$(2)$$ Newton $$-$$ Raphson method
$$(3)$$ Gauss Elimination
$$(4)$$ Simpson's Rule

The real root of the equation $$x{e^x} = 2$$ is evaluated using Newton $$-$$ Raphson's method. If the first approximation of the value of $$x$$ is $$0.8679,$$ the $${2^{nd}}$$ approximation of the value of $$x$$ correct to three decimal places is