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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.

algebra quadratic solver linear equations math helper polynomials

Formulas

For quadratic equations, the roots are calculated using:

x = b ± b2 4ac2a

The discriminant Δ determines the nature of the roots:

{
2 Real Roots if Δ > 01 Real Root if Δ = 02 Complex Roots if Δ < 0

Reference Data

Equation TypeGeneral FormSolution MethodConstraint
Linearax + b = 0Isolationa 0
Quadraticax2 + bx + c = 0Quadratic Formulaa 0
Pure Quadraticax2 + c = 0Square Rootca 0 (for Real roots)
Identity0 = 0Infinite SolutionsAlways True
Contradiction0 = k (k0)No SolutionAlways False

Frequently Asked Questions

This occurs when the discriminant (the value under the square root, b² − 4ac) is negative. In real number arithmetic, you cannot take the square root of a negative number. However, in complex analysis, this results in imaginary numbers involving i.
For optimal accuracy, yes. While the parser attempts to normalize inputs, arranging your equation as 'Expression = 0' ensures the coefficients a, b, and c are identified correctly without ambiguity.
Implicit coefficients are recognized. If a term is x², the coefficient "a" is 1. If a term is -x, the coefficient "b" is -1. The solver accounts for these standard algebraic shorthands.
If the coefficient of the squared term is zero, the equation is no longer quadratic. The system downgrades the logic to a Linear Solver automatically and solves for x using linear isolation rules.