Universal Equation Solver

A rigorous workspace for broad scalar equations and supported algebraic systems, with symbolic solving, bounded numerical refinement, and residual verification.

Equation Input

Enter an equation (e.g. 2x + 5 = 17, sin(x) = 0.5) or multiple newline-separated equations for a system.

Solver Configuration

Method

Domain

Solve for Variable(s)

Numerical Search Interval Min

Numerical Search Interval Max

Numerical Scan Segments

Displayed Precision (digits)

Maximum Roots

Capabilities & Limitations

Symbolic Pipeline

The solver normalizes ordinary or LaTeX-style input and first asks a computer-algebra engine for a finite symbolic solution set. An expression without an equals sign is interpreted as expression = 0. Symbolic parameters may remain in exact answers; numerical searches require every other parameter to have a value.

Numerical Fallback: Many equations (like $cos(x) = x$ or $x^x = 10$) have no elementary closed form. In Automatic mode, a real one-variable equation can fall back to a bounded scan that refines sign changes and tangent roots and verifies every retained candidate.

Interval Completeness

Numerical solutions are strictly bound by the configured search interval (default $[-10, 10]$). Sampling cannot prove that every root inside an arbitrary interval was found: closely spaced roots, high-frequency oscillation, or difficult discontinuities may require more scan segments or a narrower interval. No claim is made about roots outside the interval.

Unsupported Domains

This tool accepts broad, well-formed algebraic and transcendental scalar equations plus square algebraic systems that produce an isolated solution. It does not solve general ODEs, PDEs, inequalities, optimization problems, complex-plane numerical searches, or every parametric/nonlinear system branch. Unsupported and malformed inputs are reported rather than guessed.