Answer
$$x=0.26 \mathrm{m} $$
Work Step by Step
With a new value for the height $h_{0}^{\prime}=2 h_{0}=1.72 \mathrm{m},$ we solve for a new value of $x$ $\text { using the quadratic formula (taking its positive root so that } x>0)$ .
$$
m g h_{0}^{\prime}=-m g x+\frac{1}{2} k x^{2} \Rightarrow x=\frac{m g+\sqrt{b_{m g} g^{2}+2 m g k h_{0}^{\prime}}}{k}
$$
which yields $x=0.26 \mathrm{m} .$
