Help with back propagation weight computation

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I recently started studying and programming in java the back propagation algorithm based on this:

https://mattmazur.com/2015/03/17/a-step-by-step-backpropagation-example/

For now, I am just copying everything step by step so I can reproduce all the values in his article.

That being said, I am stuck on how the author obtained the values for the updated weights in the back propagation step.

On paper and in code I was able to get the correct value for $w_5^+ $ but not for the others. I know its not a bug in my code because I get the same values when I do the computation by hand, so it's something im doing incorrect with the math.

Is there any way someone could show me how he obtained the values for $w_6^+ = .408666186 , w_7^+ = .511301270, w_8^+ = .561370121$.