Math Solver — Step-by-Step
Free step-by-step math solver. Solve linear equations, quadratic equations, arithmetic expressions, and more with full working shown.
Input Examples
- Linear: 3x - 7 = 14 → x = 7
- Quadratic: x^2 - 4x - 5 = 0 → x = 5 or x = −1
- Expression: 2^10 + sqrt(144) → 1036
- System: 2x + y = 7, x - y = 2 → x = 3, y = 1
Frequently Asked Questions
- This solver handles linear equations (e.g. 2x + 5 = 11), quadratic equations (ax² + bx + c = 0), arithmetic expressions, percentage problems, and simplifications. Enter your problem in the input and the solver will detect the type and show step-by-step working.
- A linear equation has the form ax + b = c. Steps: (1) Subtract b from both sides to isolate the term with x. (2) Divide both sides by a to get x = (c − b) / a. Example: 3x + 6 = 15 → 3x = 9 → x = 3.
- For ax² + bx + c = 0, the quadratic formula is: x = (−b ± √(b² − 4ac)) / 2a. The discriminant (b² − 4ac) tells you the number of solutions: positive = 2 real roots, zero = 1 repeated root, negative = no real roots (complex).
- The discriminant is D = b² − 4ac. If D > 0: two distinct real solutions. If D = 0: one repeated solution (tangent to x-axis). If D < 0: no real solutions (parabola doesn't cross x-axis). Example: x² − 5x + 6 has D = 25 − 24 = 1 > 0, so two real roots.
- Enter each equation on a separate line in the solver. For two linear equations, the solver uses substitution or elimination. Example: 2x + y = 7 and x − y = 2. Adding them: 3x = 9 → x = 3. Substituting: y = 1.
- PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) defines the order math is evaluated. Example: 2 + 3 × 4 = 2 + 12 = 14, not 20. Always evaluate parentheses first, then exponents, then multiply/divide left-to-right, then add/subtract.
- Isolate the variable by performing inverse operations. Example — solve A = π r² for r: divide both sides by π → r² = A/π → take square root → r = √(A/π). The key rule: whatever you do to one side of the equation, you must do to the other.
- An expression is a mathematical phrase without an equals sign (e.g. 3x + 5). An equation states two expressions are equal (e.g. 3x + 5 = 11). You can simplify an expression but you solve an equation. The solver handles both — expressions are evaluated, equations are solved.
- To factor ax² + bx + c, find two numbers that multiply to a × c and add to b. Example: x² + 5x + 6 → find numbers multiplying to 6 and adding to 5 → 2 and 3 → factors are (x + 2)(x + 3). If factoring is hard, the quadratic formula always works.
- Yes — enter fractions as division: 3/4, or use decimals like 0.75. For equations with fractions, multiply through by the least common denominator to clear them before solving. Example: x/2 + 1 = 3 → multiply by 2 → x + 2 = 6 → x = 4.