Quadratic Equation Solver

The Quadratic Equation Solver solves ax^2 + bx + c = 0 and anything that reduces to it. Choose the method: Fastest lets the solver pick, Factoring finds integer or rational factors, Completing the square rewrites into vertex form and solves, Quadratic formula computes the discriminant and both roots. Whichever method you pick, the solver also reports the discriminant, the number and type of roots, the vertex, and the axis of symmetry, since those are usually the follow-up questions on the same worksheet. Equations in disguise, such as x^4 - 5x^2 + 4 = 0 or one with a fraction that clears to a quadratic, are recognised and rewritten before the method is applied.

Enter the equation in any arrangement. 2x^2 + 8x = 10 is fine; the solver moves everything to one side first and shows that step. Photographs of textbook problems work. If the problem says "solve by completing the square", set the Method option to match so the working follows the method your grader expects. Set Answer form to exact when the course wants radicals, decimal when it wants rounded values, or both. For a word problem that becomes a quadratic, such as a projectile height or an area with an unknown side, paste the whole problem; the solver sets up the equation and shows that setup before solving. Negative or non-physical roots are flagged against the context of the problem.

The output leads with the roots, then the method steps in order: rearrange, identify a, b, c, apply the method, simplify. Completing the square shows the half-and-square step explicitly. The formula method shows the discriminant computed before the roots. The working is shown so you can check it. For a polynomial of higher degree, use the Equation Solver. To sketch the parabola or find its range, use the Function Analyzer. A follow-up can rerun the same equation by a different method so you can compare the working, or convert the result between standard, factored, and vertex form. Each form is written with the steps between them.