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Free AI Quadratic Equation Solver with Steps
Solve any quadratic equation instantly with step-by-step guidance — powered by LearnFast AI.
Welcome! Ready to solve your quadratic equation step by step.
What Is a Quadratic Equation?
A quadratic equation is a second-degree polynomial equation in the form ax² + bx + c = 0, where a, b, and c are constants, and x represents the unknown variable. These equations form a parabolic curve when graphed and often appear in algebra, physics, and engineering problems.
Quadratic Equation Formula Explained
The most common method for solving any quadratic equation is the quadratic formula: x = [-b ± √(b² – 4ac)] / 2a This formula works for all types of quadratic equations, even when factoring is difficult or impossible. Just plug in the values of a, b, and c and follow the steps shown by our AI solver.
Key Features of LearnFast AI Quadratic Equation Solver
Input Support for Standard Quadratic Form
You can enter equations like 2x² - 4x + 1 = 0, including fractions, decimals, and negatives. Our AI quadratic equation solver also lets you upload handwritten or printed equations as images for instant analysis.
Step-by-Step Quadratic Equation Solver with Explanations
Unlike tools that only show the final answer, our quadratic equation solver with steps breaks down every part of the process. Learn how to break down terms, apply formulas accurately, and interpret your results effectively with the help of the AI Math Calculator.
Multiple Quadratic Equation Solving Methods
Our tool supports the quadratic formula, factoring, and completing the square. You can compare different methods and choose the one that best fits your learning style or assignment requirements.
Free Online Quadratic Equation Solver – No Login Needed
Solving quadratic equations is free to try on LearnFast AI. There's no sign-up, no subscription, and no installation—just open the tool and start solving.
How to Solve Quadratic Equations in 3 Simple Steps
Step 1: Enter Your Equation
Type your quadratic equation in the input box or upload a photo of your math problem. Our AI supports all standard quadratic forms, including those with decimals or fractions.
Solving Quadratic Equations with AI
Use the default quadratic formula or try factoring and completing the square for different approaches. You can also specify your preferred method when entering the equation—for example, type “solve by factoring” or “use quadratic formula” to guide the solver.
Step 3: Get Step-by-Step Solutions
Receive a full breakdown of the solution process, helping you learn the logic behind each calculation. Great for both understanding and accuracy.
Quadratic Equation Examples – Solve for x with Clarity
Example 1: Simple Factoring
x² - 5x + 6 = 0 This classic equation can be factored into (x - 2)(x - 3), giving x = 2 or x = 3. A great way to introduce factoring with our solve quadratic equation calculator.
Example 2: Chemistry Reaction Rate Problem
0.1x² + 0.5x - 0.2 = 0 Used to model the concentration of a substance over time, this equation is best solved using the quadratic formula for precise results.
Example 3: Physics Projectile Motion
-4.9x² + 12x + 2 = 0 Describes the height of an object over time. Try this in our AI quadratic equation solver to find time of flight and peak height.
Example 4: Understand the Quadratic Equation While Solving It
What does a quadratic equation mean? Our quadratic equation solver doesn’t just give you the final answer—it helps you understand what a quadratic equation is, how it works, and why each step matters. It’s a learning tool as much as a calculator.
Who Can Benefit from LearnFast AI Quadratic Equation Solver
🎓 Students
Perfect for high school and college students who want instant homework help or deeper understanding of how to solve quadratic equations step-by-step.
📚 Teachers and Tutors
Use our AI tool in the classroom or tutoring sessions to demonstrate multiple solving methods and ensure clarity in every step.
🤖 Self-Learners
Whether you're preparing for exams or brushing up on math skills, this free quadratic equation solver helps you learn at your own pace.
📐 Engineers & Professionals
Quickly solve quadratic expressions that appear in physics, engineering, or financial models — with no need for manual calculations.
User Feedback on Our AI Quadratic Equation Calculator
This AI solver helped me finally understand how the quadratic formula works. The steps are super clear and easy to follow!
Emily R.
High School Student
I use LearnFast AI's quadratic equation solver in every tutoring session. It’s a game-changer for visual learners.
James L.
Private Tutor
I uploaded a photo of a handwritten problem, and it solved it instantly. Love how it supports decimals and explains each step!
Priya S.
College Freshman
When I'm working with motion formulas, this AI solver saves me so much time. Fast, accurate, and free.
Carlos D.
Mechanical Engineer
I’m re-learning algebra after many years. This solver gives me confidence and makes studying manageable.
Zoe K.
Adult Learner
Great tool for showing students different ways to solve the same quadratic. The UI is simple and efficient.
Arjun M.
Math Teacher
Frequently Asked Questions
How to solve quadratic equation by quadratic formula step by step?
To solve ax² + bx + c = 0, use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. First, identify a, b, and c, then calculate the discriminant. Plug the values into the formula and simplify. You can also use LearnFast AI’s solver for a quick and accurate solution. Our AI tool guides you through each step, making it easy to understand without a math degree. Try it now!
Can AI solve quadratic equations?
Yes! LearnFast AI’s quadratic equation solver solves equations, explains steps, and handles fractions, decimals, and negatives—free and no login required.
What is the best way to solve a quadratic equation?
The quadratic formula is the most reliable method. Use LearnFast AI’s solver for quick and accurate solutions, applying the formula when appropriate.
Can I solve a quadratic equation using a photo?
Yes! You can upload an image of a handwritten or printed problem, and our AI quadratic equation solver will recognize and solve it.
Is LearnFast AI’s quadratic equation solver really free?
Absolutely. You can solve unlimited quadratic equations for free — no login or subscription required. Try it now!
Does the solver provide step-by-step solutions?
Yes, it shows every calculation in detail — ideal for learning and reviewing how quadratic equations are solved.
Can the AI handle fractions and decimals?
Definitely. Our solver supports all common number formats, including fractions, decimals, and negatives.
Does it work on mobile devices?
Yes, our utility page is mobile-friendly, so you can solve quadratic equations on the go using your phone or tablet.