# Equation Steps

> Step-by-step solver for linear/quadratic equations in one variable, signs and ± always right.

- name: com.gumballtools/equation-steps
- version: 0.1.0
- connection class: R0 (autonomous)
- trust: 89/100 flags: duplicate-repo
- quality: 86/100 (good)
- owner: not claimed
- descriptor: https://api.protogrid.dev/v1/servers/com.gumballtools%2Fequation-steps
- tools: https://api.protogrid.dev/v1/servers/com.gumballtools%2Fequation-steps/tools

**An agent can connect right now, no human step.** Remote endpoint, no authentication, reachable on the last probe.

## Connection (mcpServers)

```json
{
  "mcpServers": {
    "equation-steps": {
      "type": "http",
      "url": "https://equation-steps.gumballtools.com/api/mcp"
    }
  }
}
```


## Trust

- hygiene: 80
- liveness: 100
- freshness: 85
- provenance: 85
- drivers: +repository +dns-namespace +website +reachable +uptime-100% ~updated-44d-ago -duplicate-repo(16 names)
- Derived from observable signals (official registry feed and our own credential-free probes); no code audit performed.

## Quality 86/100 (good)

### protocol: 88 (weight 25)

- pass `protocol.modern`: supports 2026-07-28 (server/discover)
- pass `protocol.stateless`: answers without a session
- pass `protocol.transport`: streamable HTTP
- warn `protocol.list_ttl`: tools/list declares ttlMs 0, so clients re-fetch it on every use

### authorization: n/a (weight 15)

- n/a `auth.prm`, `auth.as_metadata`, `auth.cimd`: no remote uses OAuth
- n/a `auth.secret_in_url`: no templated URL

### tool hygiene: 79 (weight 30)

- pass `tools.descriptions`: every tool has a description
- warn `tools.description_length`: 1 tools have descriptions over 1,024 characters, which crowds the context
- pass `tools.schemas`: every tool has an object input schema
- pass `tools.annotations`: 1 of 1 tools declare readOnlyHint or destructiveHint
- fail `tools.directory_hints`: no tool declares all four of readOnlyHint, destructiveHint, idempotentHint and openWorldHint; missing: run (destructiveHint, idempotentHint)
- pass `tools.token_cost`: about 532 tokens to load every tool
- pass `tools.api_dump`: tools are not a one-to-one API dump

### stability: 100 (weight 15)

- pass `stability.changes`: no tool changes in 30 days
- pass `stability.rug_pull`: no tool changed its meaning under the same name

### dependencies: n/a (weight 15)

- n/a `deps.known_vulns`, `deps.mcp_sdk_version`, `deps.resolvable`: no npm or PyPI package

- tools: 1, about 532 tokens to load them all
- tool set hash: 947f44d417cc99d9c3d610994cdc7d77
- badge: [![protogrid quality](https://protogrid.dev/badge/com.gumballtools/equation-steps.svg)](https://protogrid.dev/servers/com.gumballtools/equation-steps)
- Checks run on what our credential-free, read-only probes observe; tools are never called and no code audit is performed.

### Tool changes

_No tool definition changes recorded._

## Remotes

- https://equation-steps.gumballtools.com/api/mcp (streamable-http, auth none, reachable true, uptime30d 1)

## Packages

_none_

## Tools (1)

- `run`: Solves a linear or quadratic equation in one variable (x) and returns every step: expanding parentheses, combining like terms, moving terms across the equals sign, and (for quadratics) applying the quadratic formula.

Use this whenever you need to solve "ax + b = cx + d" or "ax^2 + bx + c = 0" style equations, or check a step-by-step algebra solution someone else produced.

Do not solve this kind of equation by reasoning through it token by token: the two places language models most often go quietly wrong are (1) the sign when distributing a negative across parentheses, e.g. "5 - (x - 3)" losing the minus on the 3, and (2) dropping one of the two ± roots of a quadratic, or rounding a complex root into a false "no solution". This tool always gets both right because it does exact fraction arithmetic, not floating-point guessing, and reports every root it finds — including complex ones, explicitly labeled as complex.

Input: a single string containing exactly one "=", using x (or X) as the only variable, e.g. "3(x-2) = 5x + 4" or "(x+1)(x-3) = 2x^2 - 5". Numbers may be integers or decimals. Implicit multiplication is fine ("3x", "2(x+1)"). Exponents may only be "^2" on the bare variable — "(x+1)^2" is not supported; write "(x+1)(x+1)" instead.

Refuses rather than guesses on: no "=" or more than one, a second variable or a function name (sin, sqrt, log), a "/" anywhere (rewrite as a decimal), an unsupported exponent, an equation that expands past degree 2, unbalanced parentheses, or an inequality (<, >). Every refusal includes a fixHint saying exactly what to change.

Returns the equation type (linear, quadratic, identity, or contradiction), the standard form, the full list of steps, the solution(s) as exact fractions (with a decimal alongside when not a whole number), and a disclaimer that this covers only one-variable linear and quadratic equations.