Algebra Calculator.
Solve linear and quadratic equations, simplify expressions, and understand algebra with interactive visualizations and step-by-step solutions.
Choose Equation Type
Linear Equation
Equation Visualization
Step-by-Step Solution
See exactly how the equation is solved
Understanding the Solution
Linear Equation: 2x + 5 = 15
Step 1: Subtract 5 from both sides: 2x = 10
Step 2: Divide both sides by 2: x = 5
Result: x = 5
Smart Insights
Discover useful algebra facts and applications
Real-World Application
Algebra is used in physics, engineering, economics, computer science, and everyday problem-solving. It helps model and solve real-world problems.
Quick Tip
Always check your solution by substituting it back into the original equation. If both sides are equal, your answer is correct!
Common Mistake
When moving terms across the equals sign, remember to change the operation: addition becomes subtraction, and multiplication becomes division.
Interesting Fact
The quadratic formula (x = (-b ± √(b²-4ac)) / 2a) can solve ANY quadratic equation, no matter how complex!
Understanding Algebra
Linear Equations
A linear equation has the form ax + b = c, where a, b, and c are constants. The solution is x = (c - b) / a. Linear equations represent straight lines when graphed.
Quadratic Equations
A quadratic equation has the form ax² + bx + c = 0. Solutions can be found using factoring, completing the square, or the quadratic formula: x = (-b ± √(b²-4ac)) / 2a
The Quadratic Formula
The discriminant (b²-4ac) determines the nature of roots: positive = two real roots, zero = one repeated root, negative = two complex roots.
Algebraic Operations
- Addition: Combine like terms
- Distribution: a(b + c) = ab + ac
- Factoring: Reverse of distribution
- Division: Divide both sides equally
Frequently Asked Questions
What is the quadratic formula?
The quadratic formula is x = (-b ± √(b²-4ac)) / 2a. It solves any equation of the form ax² + bx + c = 0. The ± symbol means there can be two solutions.
What does the discriminant tell us?
The discriminant (b²-4ac) tells us about the roots: if positive, there are two distinct real roots; if zero, there's one repeated real root; if negative, there are two complex roots.
How do I check if my solution is correct?
Substitute your solution back into the original equation. If both sides are equal, your answer is correct. For example, if x = 5 solves 2x + 5 = 15, then 2(5) + 5 = 15, which is true.
What are like terms?
Like terms are terms with the same variable raised to the same power. For example, 3x and 5x are like terms (can be combined to 8x), but 3x and 3x² are not.
Why is algebra important?
Algebra provides a systematic way to solve problems with unknown quantities. It's the foundation for advanced math, science, engineering, and technology.