I quote the next verse:
Php 2:13 For it is God which worketh in you both to will and to do of his good pleasure.
And also to point out that to "work out your own salvation" has more to do with performing those acts which accompany it, but do not earn it:
Rom_4:4 Now to him that worketh is the reward not reckoned of grace, but of debt.
It is still up to us as Christians to make decisions based on the Word - obedience is what God desires. He prompts us with Scripture when needed. This reminds me of a little boy whose mother told him to bring the broom in from the back porch late one night. HE was scared of the dark - so she told him - “don’t worry - God will help you.” So, the little boy stuck his hand out the back door and said - “God, hand me the broom.” We still have to put legs to our faith.