Algebraic equations are mathematical statements that assert the equality of two expressions. They typically involve variables (represented by letters like 'x', 'y', 'a', 'b') and constants (numbers). The goal of solving an algebraic equation is to find the value(s) of the variable(s) that make the equation true.
Types of Algebraic Equations
Algebraic equations can range in complexity. Some common types include:
Linear Equations: Equations where the highest power of the variable is 1. They typically have the form ax + b = c.
Quadratic Equations: Equations where the highest power of the variable is 2. They typically have the form ax² + bx + c = 0.
Polynomial Equations: Equations involving higher powers of variables.
How This Calculator Works
This calculator is designed to solve simple linear equations of the form ax + b = c. It works by isolating the variable 'x' through a series of algebraic manipulations:
Subtract 'b' from both sides:ax = c - b
Divide both sides by 'a':x = (c - b) / a
For more complex equations (like quadratic equations or those with multiple variables), specialized methods such as factoring, completing the square, the quadratic formula, or matrix methods would be required. This calculator focuses on the fundamental linear form for simplicity and clarity.
Example
Let's solve the equation 3x + 6 = 18:
3x + 6 = 18
1. Subtract 6 from both sides:
3x = 18 – 6
3x = 12
2. Divide both sides by 3:
x = 12 / 3
x = 4
Therefore, the solution is x = 4. You can enter this equation into the calculator above to verify.
Use Cases
Understanding and solving algebraic equations is fundamental in many fields:
Mathematics Education: Essential for learning core mathematical concepts.
Science and Engineering: Used to model physical phenomena, design systems, and analyze data.
Computer Science: Underpins algorithms, data structures, and programming logic.
Economics and Finance: Models market behavior, investment strategies, and financial planning.
Everyday Problem Solving: Helps in budgeting, planning, and making logical decisions.
function solveEquation() {
var equationInput = document.getElementById("equation");
var solutionDisplay = document.getElementById("solutionDisplay");
var equationString = equationInput.value.trim();
solutionDisplay.textContent = "Processing…";
if (equationString === "") {
solutionDisplay.textContent = "Please enter an equation.";
return;
}
// Attempt to parse and solve linear equations of the form ax + b = c or ax – b = c
// Regex to capture coefficients and constants for ax + b = c or ax – b = c
// It looks for patterns like: number x sign number = number
// Example: "2x + 5 = 13", "3x – 7 = 11", "x + 2 = 5", "4x = 12"
var linearMatch = equationString.match(/^(-?\d*\.?\d*)x\s*([+-])\s*(\d+\.?\d*)\s*=\s*(-?\d+\.?\d*)$/i);
var simpleLinearMatch = equationString.match(/^(-?\d*\.?\d*)x\s*=\s*(-?\d+\.?\d*)$/i);
var form_ax_plus_b_equals_c = equationString.match(/^(-?\d*\.?\d*)x\s*\+\s*(\d+\.?\d*)\s*=\s*(-?\d+\.?\d*)$/i);
var form_ax_minus_b_equals_c = equationString.match(/^(-?\d*\.?\d*)x\s*-\s*(\d+\.?\d*)\s*=\s*(-?\d+\.?\d*)$/i);
var form_x_plus_b_equals_c = equationString.match(/^(x)\s*\+\s*(\d+\.?\d*)\s*=\s*(-?\d+\.?\d*)$/i);
var form_x_minus_b_equals_c = equationString.match(/^(x)\s*-\s*(\d+\.?\d*)\s*=\s*(-?\d+\.?\d*)$/i);
var a = 0, b = 0, c = 0;
var xCoefficient = 1; // Default for cases like 'x + 5 = 10'
if (simpleLinearMatch) {
// Case: ax = c
a = parseFloat(simpleLinearMatch[1]);
c = parseFloat(simpleLinearMatch[2]);
if (isNaN(a) || isNaN(c)) {
solutionDisplay.textContent = "Invalid numbers in equation.";
return;
}
if (a === 0) {
solutionDisplay.textContent = "Coefficient 'a' cannot be zero for ax=c.";
return;
}
var x = c / a;
solutionDisplay.textContent = `x = ${x}`;
return;
}
if (form_ax_plus_b_equals_c) {
// Case: ax + b = c
a = parseFloat(form_ax_plus_b_equals_c[1]);
b = parseFloat(form_ax_plus_b_equals_c[2]);
c = parseFloat(form_ax_plus_b_equals_c[3]);
if (isNaN(a) || isNaN(b) || isNaN(c)) {
solutionDisplay.textContent = "Invalid numbers in equation.";
return;
}
if (a === 0) {
solutionDisplay.textContent = "Coefficient 'a' cannot be zero.";
return;
}
// ax + b = c => ax = c – b => x = (c – b) / a
var x = (c – b) / a;
solutionDisplay.textContent = `x = ${x}`;
return;
}
if (form_ax_minus_b_equals_c) {
// Case: ax – b = c
a = parseFloat(form_ax_minus_b_equals_c[1]);
b = parseFloat(form_ax_minus_b_equals_c[2]);
c = parseFloat(form_ax_minus_b_equals_c[3]);
if (isNaN(a) || isNaN(b) || isNaN(c)) {
solutionDisplay.textContent = "Invalid numbers in equation.";
return;
}
if (a === 0) {
solutionDisplay.textContent = "Coefficient 'a' cannot be zero.";
return;
}
// ax – b = c => ax = c + b => x = (c + b) / a
var x = (c + b) / a;
solutionDisplay.textContent = `x = ${x}`;
return;
}
if (form_x_plus_b_equals_c) {
// Case: x + b = c
b = parseFloat(form_x_plus_b_equals_c[2]);
c = parseFloat(form_x_plus_b_equals_c[3]);
if (isNaN(b) || isNaN(c)) {
solutionDisplay.textContent = "Invalid numbers in equation.";
return;
}
// x + b = c => x = c – b
var x = c – b;
solutionDisplay.textContent = `x = ${x}`;
return;
}
if (form_x_minus_b_equals_c) {
// Case: x – b = c
b = parseFloat(form_x_minus_b_equals_c[2]);
c = parseFloat(form_x_minus_b_equals_c[3]);
if (isNaN(b) || isNaN(c)) {
solutionDisplay.textContent = "Invalid numbers in equation.";
return;
}
// x – b = c => x = c + b
var x = c + b;
solutionDisplay.textContent = `x = ${x}`;
return;
}
// If none of the specific linear forms match, provide a generic message.
// This calculator is simplified and only handles basic linear equations.
solutionDisplay.textContent = "Unsupported equation format. Please use the form 'ax + b = c' or 'ax = c'.";
}