Home › Math & Conversions › Core Math & Algebra › Equation Solver Equation Solver Solve linear and quadratic equations, or small systems of equations, with step-by-step explanations and a numeric root finder for general equations of the form f(x) = 0. Single equation System of equations Equation in one variable (x) Use x as the variable and ^ for powers (e.g., x^2 ). You can also enter equations like sin(x) - x/2 = 0 for the numeric solver. Solving method Auto detect (linear/quadratic first) Linear (ax + b = c) Quadratic (ax^2 + bx + c = 0) Numeric (Newton–Raphson) Initial guess (numeric mode) Used only for the numeric solver. Tolerance Smaller values require more iterations. Solve equation Clear The solution and step-by-step explanation will appear here. Solve a small linear system in the form Ax = b. Enter the coefficients and constants for each equation. System size 2 × 2 system (variables x, y) 3 × 3 system (variables x, y, z) Equation x y z = Constant 1 = 2 = 3 = For a 2×2 system, only the first two rows and the x, y columns are used. The third row and z column are ignored. Solve system Clear The solution and intermediate matrix steps will appear here. How this equation solver works This tool is designed for core algebra and pre-calculus work. It combines exact algebraic formulas for linear and quadratic equations with a numeric solver for more general problems, plus a compact linear system solver for small systems. 1. Linear equations in one variable A linear equation in one variable has the form ax + b = c , where a , b , and c are real numbers and a ≠ 0 . Solving a linear equation: Start from: ax + b = c Subtract b from both sides: ax = c - b Divide by a : x = (c - b)

Subcategories in Home › Math & Conversions › Core Math & Algebra › Equation Solver Equation Solver Solve linear and quadratic equations, or small systems of equations, with step-by-step explanations and a numeric root finder for general equations of the form f(x) = 0. Single equation System of equations Equation in one variable (x) Use x as the variable and ^ for powers (e.g., x^2 ). You can also enter equations like sin(x) - x/2 = 0 for the numeric solver. Solving method Auto detect (linear/quadratic first) Linear (ax + b = c) Quadratic (ax^2 + bx + c = 0) Numeric (Newton–Raphson) Initial guess (numeric mode) Used only for the numeric solver. Tolerance Smaller values require more iterations. Solve equation Clear The solution and step-by-step explanation will appear here. Solve a small linear system in the form Ax = b. Enter the coefficients and constants for each equation. System size 2 × 2 system (variables x, y) 3 × 3 system (variables x, y, z) Equation x y z = Constant 1 = 2 = 3 = For a 2×2 system, only the first two rows and the x, y columns are used. The third row and z column are ignored. Solve system Clear The solution and intermediate matrix steps will appear here. How this equation solver works This tool is designed for core algebra and pre-calculus work. It combines exact algebraic formulas for linear and quadratic equations with a numeric solver for more general problems, plus a compact linear system solver for small systems. 1. Linear equations in one variable A linear equation in one variable has the form ax + b = c , where a , b , and c are real numbers and a ≠ 0 . Solving a linear equation: Start from: ax + b = c Subtract b from both sides: ax = c - b Divide by a : x = (c - b).

a 2. Quadratic equations A quadratic equation has the form ax^2 + bx + c = 0 with a ≠ 0 . The solutions are given by the quadratic formula. Quadratic formula: Given ax^2 + bx + c = 0 , define the discriminant D = b^2 - 4ac . If D > 0 , there are two distinct real roots. If D = 0 , there is one repeated real root. If D < 0 , the roots are complex conjugates. The roots are: x = (-b ± √D)

1 calculators