General Equation Solver
Universal algebra tool for linear and quadratic equations. Features smart recognition to auto-detect equation types and apply specific solving algorithms.
About
Students and engineers often face the tedious task of isolating variables in algebraic expressions. This tool automates the process for linear and quadratic forms. It eliminates manual rearrangement errors by parsing the input string directly. The solver identifies the degree of the polynomial and selects the appropriate algorithm, such as the Quadratic Formula for degree 2 equations. Accuracy is paramount here because a sign error in the discriminant calculation renders the entire solution set invalid.
The underlying engine parses standard forms like ax + b = 0 and ax2 + bx + c = 0. It handles coefficients, constant terms, and zero-equated expressions. This functionality serves as a verification layer for manual homework or a rapid calculation utility for system modeling.
Formulas
For quadratic equations, the roots are calculated using:
The discriminant Δ determines the nature of the roots:
Reference Data
| Equation Type | General Form | Solution Method | Constraint |
|---|---|---|---|
| Linear | ax + b = 0 | Isolation | a ≠ 0 |
| Quadratic | ax2 + bx + c = 0 | Quadratic Formula | a ≠ 0 |
| Pure Quadratic | ax2 + c = 0 | Square Root | −ca ≥ 0 (for Real roots) |
| Identity | 0 = 0 | Infinite Solutions | Always True |
| Contradiction | 0 = k (k≠0) | No Solution | Always False |