Enter your algebraic equation below. This calculator can solve for a single variable (typically 'x').
Your solution will appear here.
Understanding Algebraic Equations and Solvers
Algebraic equations are fundamental to mathematics, forming the basis for problem-solving across countless disciplines. An algebraic equation is a mathematical statement that asserts the equality of two expressions. These expressions can contain numbers, variables (like 'x', 'y', 'z'), and mathematical operations (addition, subtraction, multiplication, division, exponents, etc.).
The primary goal when solving an algebraic equation is to find the value(s) of the variable(s) that make the equation true. This process is known as finding the "roots" or "solutions" of the equation.
How Algebraic Solvers Work (The Math Behind the Calculator)
This free algebra solver aims to simplify and solve linear equations of the form ax + b = c, or slightly more complex variations where the variable 'x' might appear on both sides of the equation. The core principle is to isolate the variable 'x' on one side of the equation. This is achieved by applying inverse operations to both sides of the equation to maintain equality.
Addition/Subtraction: If a number is added to the term with 'x', subtract it from both sides. If it's subtracted, add it to both sides.
Multiplication/Division: If 'x' is multiplied by a number, divide both sides by that number. If 'x' is divided by a number, multiply both sides by that number.
Rearranging Terms: Often, terms involving 'x' need to be gathered on one side, and constant terms on the other.
For example, to solve 2x + 5 = 17:
Subtract 5 from both sides: 2x + 5 - 5 = 17 - 5 which simplifies to 2x = 12.
Divide both sides by 2: 2x / 2 = 12 / 2 which simplifies to x = 6.
So, the solution is x = 6.
Use Cases for an Algebra Equation Solver:
A free algebra equation solver is an invaluable tool for:
Students: To check homework, understand equation manipulation, and gain confidence in solving problems.
Educators: To quickly generate solutions for practice problems or to demonstrate equation solving techniques.
Professionals: In fields like engineering, physics, economics, and computer science, where quick calculations and variable isolation are frequently required.
Hobbyists: Anyone needing to solve mathematical problems in personal projects or learning endeavors.
While this calculator is designed for common linear equations, advanced algebra involves quadratic equations, polynomial equations, and systems of equations, which require more sophisticated solving techniques. However, mastering linear equations is a crucial first step.
function solveEquation() {
var equationString = document.getElementById("equation").value.trim();
var resultDiv = document.getElementById("result");
// Clear previous results
resultDiv.textContent = "Solving…";
if (!equationString) {
resultDiv.textContent = "Please enter an equation.";
return;
}
try {
// — Basic Linear Equation Solver Logic —
// This is a simplified solver. It's designed to handle basic linear equations
// of the form ax + b = c or ax + b = cx + d.
// It's not a full-fledged symbolic math engine.
// Normalize the equation: replace '=' with '-=' for easier processing if '=' is present
if (equationString.includes('=')) {
var parts = equationString.split('=');
if (parts.length !== 2) {
throw new Error("Invalid equation format: multiple '=' signs.");
}
// Rearrange to form LHS – RHS = 0
equationString = parts[0].trim() + ' – (' + parts[1].trim() + ')';
}
// Attempt to parse and simplify the expression to isolate 'x'
// This is a very naive approach and will only work for simple cases.
// For robustness, a proper parser and symbolic manipulation library would be needed.
// Let's try to evaluate coefficients for 'x' and constant terms.
// We'll look for terms like 'ax' or 'x' and sum their coefficients,
// and sum constant terms.
var xCoefficient = 0;
var constantTerm = 0;
// Replace 'x' with '+1*x' or '-1*x' to handle cases like 'x' or '-x'
equationString = equationString.replace(/\b(x)\b/g, '1*x');
equationString = equationString.replace(/\b(-x)\b/g, '-1*x');
// Ensure operations are explicit for multiplication (e.g., 2x -> 2*x)
equationString = equationString.replace(/(\d)([a-zA-Z])/g, '$1*$2'); // 2x -> 2*x
equationString = equationString.replace(/([a-zA-Z])(\d)/g, '$1*$2'); // x2 -> x*2
equationString = equationString.replace(/([\*\+\-\/])([a-zA-Z])/g, '$11*$2'); // +x -> +1*x, -x -> -1*x
// Split the expression into terms
var terms = equationString.match(/[+-]?\s*(?:\d*\.?\d+|\d*\.?\d*x)/g);
if (!terms) {
throw new Error("Could not parse equation terms.");
}
for (var i = 0; i < terms.length; i++) {
var term = terms[i].trim().replace(/\s/g, ''); // Remove spaces within term
if (term.includes('x')) {
var coefficientStr = term.replace('x', '');
if (coefficientStr === '' || coefficientStr === '+') {
xCoefficient += 1;
} else if (coefficientStr === '-') {
xCoefficient -= 1;
} else {
xCoefficient += parseFloat(coefficientStr);
}
} else {
constantTerm += parseFloat(term);
}
}
// Now we have an equation of the form: xCoefficient * x + constantTerm = 0
// Isolate x: xCoefficient * x = -constantTerm
// x = -constantTerm / xCoefficient
if (isNaN(xCoefficient) || isNaN(constantTerm)) {
throw new Error("Invalid numerical values in equation.");
}
if (xCoefficient === 0) {
if (constantTerm === 0) {
resultDiv.textContent = "Infinite solutions (identity).";
} else {
resultDiv.textContent = "No solution (contradiction).";
}
} else {
var solution = -constantTerm / xCoefficient;
if (isNaN(solution)) {
throw new Error("Calculation resulted in NaN.");
}
// Format solution for better readability, avoid excessive decimals if integer
if (Number.isInteger(solution)) {
resultDiv.textContent = "x = " + solution;
} else {
resultDiv.textContent = "x = " + solution.toFixed(5).replace(/\.?0+$/, ''); // Remove trailing zeros
}
}
} catch (error) {
console.error("Error solving equation:", error);
resultDiv.textContent = "Error: " + error.message;
}
}