Equation Solver
Solve linear and quadratic equations.
Algebra is the foundation of higher mathematics, and at its heart lies the art of solving equations. An equation solver is a powerful tool designed to find the value(s) of a variable (often 'x') that make an equation true. This calculator is built to handle two of the most common types of algebraic equations: linear and quadratic equations. This guide will explain how it works, the formulas it uses, and how to interpret the results.
How to Use the Equation Solver
Using the solver is simple. Type your equation into the input box, ensuring it is set equal to zero. The calculator recognizes standard algebraic notation.
- For Linear Equations: Use the format
ax+b=0. For example,3x-9=0. - For Quadratic Equations: Use the format
ax^2+bx+c=0. Use the caret symbol (^) for the exponent. For example,2x^2-3x-5=0.
The solver will parse the coefficients (a, b, and c), identify the type of equation, and provide the roots (solutions) along with the step-by-step process.
Solving Linear Equations
A linear equation is an equation of the first degree, meaning the highest power of the variable is 1. The goal is to isolate 'x'.
Given: ax + b = 0
Solution: x = -b / a
Solving Quadratic Equations: The Quadratic Formula
A quadratic equation is an equation of the second degree (highest power is 2). These equations can have two real roots, one real root, or two complex roots. The solver uses the quadratic formula, a cornerstone of algebra, to find these roots.
For an equation ax² + bx + c = 0, the roots are given by:
x = [-b ± √(b² - 4ac)] / 2a
The expression inside the square root, b² - 4ac, is called the **discriminant (Δ)**. The value of the discriminant tells us the nature of the roots:
- If Δ > 0: There are two distinct real roots. The parabola crosses the x-axis at two different points.
- If Δ = 0: There is exactly one real root (a repeated root). The vertex of the parabola touches the x-axis at one point.
- If Δ < 0: There are no real roots. The roots are two complex conjugate numbers. The parabola does not cross the x-axis. This calculator will show you these complex roots.
This equation solver simplifies the process of finding solutions, providing not just the answer but also the clear, logical steps required to reach it, making it a valuable tool for students and professionals alike.
Enter values to see the results.
Algebra is the foundation of higher mathematics, and at its heart lies the art of solving equations. An equation solver is a powerful tool designed to find the value(s) of a variable (often 'x') that make an equation true. This calculator is built to handle two of the most common types of algebraic equations: linear and quadratic equations. This guide will explain how it works, the formulas it uses, and how to interpret the results.
How to Use the Equation Solver
Using the solver is simple. Type your equation into the input box, ensuring it is set equal to zero. The calculator recognizes standard algebraic notation.
- For Linear Equations: Use the format
ax+b=0. For example,3x-9=0. - For Quadratic Equations: Use the format
ax^2+bx+c=0. Use the caret symbol (^) for the exponent. For example,2x^2-3x-5=0.
The solver will parse the coefficients (a, b, and c), identify the type of equation, and provide the roots (solutions) along with the step-by-step process.
Solving Linear Equations
A linear equation is an equation of the first degree, meaning the highest power of the variable is 1. The goal is to isolate 'x'.
Given: ax + b = 0
Solution: x = -b / a
Solving Quadratic Equations: The Quadratic Formula
A quadratic equation is an equation of the second degree (highest power is 2). These equations can have two real roots, one real root, or two complex roots. The solver uses the quadratic formula, a cornerstone of algebra, to find these roots.
For an equation ax² + bx + c = 0, the roots are given by:
x = [-b ± √(b² - 4ac)] / 2a
The expression inside the square root, b² - 4ac, is called the **discriminant (Δ)**. The value of the discriminant tells us the nature of the roots:
- If Δ > 0: There are two distinct real roots. The parabola crosses the x-axis at two different points.
- If Δ = 0: There is exactly one real root (a repeated root). The vertex of the parabola touches the x-axis at one point.
- If Δ < 0: There are no real roots. The roots are two complex conjugate numbers. The parabola does not cross the x-axis. This calculator will show you these complex roots.
This equation solver simplifies the process of finding solutions, providing not just the answer but also the clear, logical steps required to reach it, making it a valuable tool for students and professionals alike.