Algebra Calculator

Algebra Equations:

\[ ax + b = c \] \[ ax^2 + bx + c = 0 \] \[ a^x = b \]

Equation Type:

Coefficient (a):

Constant (b):

Right Side (c):

Coefficient a:

Coefficient b:

Constant c:

Base (a):

Right Side (b):

Solution:

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1. What is the Algebra Calculator?

The Algebra Calculator solves various types of algebraic equations including linear, quadratic, and exponential equations. It provides step-by-step solutions to help understand the solving process.

2. How Does the Calculator Work?

The calculator uses mathematical algorithms to solve equations:

Linear: \( ax + b = c \) → \( x = \frac{c - b}{a} \)

Quadratic: \( ax^2 + bx + c = 0 \) → \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

Exponential: \( a^x = b \) → \( x = \frac{\ln b}{\ln a} \)

3. Types of Equations Supported

Linear Equations: First-degree equations in the form ax + b = c

Quadratic Equations: Second-degree equations in the form ax² + bx + c = 0

Exponential Equations: Equations with variables in exponents in the form a^x = b

4. Using the Calculator

Steps: Select equation type, enter coefficients, and click Calculate. The solution will be displayed with real and complex roots as appropriate.

5. Frequently Asked Questions (FAQ)

Q1: What if I get complex numbers as solutions?
A: Some quadratic equations have complex roots when the discriminant is negative. These are valid mathematical solutions.

Q2: Why does my exponential equation need positive base?
A: The calculator uses logarithms which require positive base numbers (a > 0, a ≠ 1).

Q3: What does "No solution" mean?
A: This appears when the equation is impossible (e.g., 0x = 5) or has no real solutions.

Q4: How precise are the solutions?
A: Solutions are rounded to 4 decimal places for readability.

Q5: Can I solve systems of equations?
A: This calculator currently solves single equations only.