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Given the progression as detailed in this image:

Xp Progression

What is the formula that expresses: when x = totalXP gives the result of y = LVL?

For example, knowing I have 1000XP I solve the formula entering 1000xp and the result would be lvl 4.

Thanks!

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    $\begingroup$ Welcome to Math.SE! Please refrain from posting without any context. You can do this by stating the origin of your question or showing your attempts to solve it. $\endgroup$
    – soupless
    Jul 23, 2021 at 16:26
  • $\begingroup$ @soupless thank you! What context do you require? I am just not good at math so I have no idea how to solve this. I am happy to answer any clarifying questions if the initial question was unclear, thanks for your help $\endgroup$
    – fabrialis
    Jul 23, 2021 at 16:30
  • $\begingroup$ @soupless I can give you an example, to find out XPneeded : XPneeded =LvL*100, so if I know that LvL = 5 then XPneeded = 500. Now I am trying to find the formula for: LVL = XPTotal * ???, which would give me the current lvl for a given XpTotal $\endgroup$
    – fabrialis
    Jul 23, 2021 at 16:34
  • $\begingroup$ You need to state the origin of your question. Where did it came from? A textbook? Online resource? Also, you need to include your attempt(s) to solve the question, even if it failed. That way, others can provide better insights that can help you. Because you did not do this as of the moment, your question attracted some downvotes as questions like this are low quality. $\endgroup$
    – soupless
    Jul 23, 2021 at 16:34

1 Answer 1

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You can set up a quadratic equation. Let $T$ be the "Total XP" and $n$ the index of $LVL(n)$. Then the equation is

\begin{align*} & 100\cdot \sum\limits_{i=0}^{n} i=T\\ &100\cdot \frac{n\cdot (n+1)}{2}=T \\ &n\cdot (n+1)=\frac{T}{50} \\ & n\cdot (n+1)-\frac{T}{50}=0\\ \end{align*}

This is a quadratic equation, which can be solved with the quadratic formula. It comes out that the positive solution is

$$n=\frac{-1+\sqrt{1+\frac{4\cdot T}{50}}}{2}$$

Numerical example for $T=1500$

\begin{align*} & n=\frac{-1+\sqrt{1+\frac{4\cdot 1500}{50}}}{2}\\ & n=\frac{-1+\sqrt{1+120}}{2} \\ & n=\frac{-1+\sqrt{121}}{2}=\frac{-1+\sqrt{121}}{2}=\frac{10}2=5\end{align*}

If Total XP is $1500$ then the index of LVL(n) is $5$.

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