About this completing the square calculator
This completing the square calculator helps you rewrite a quadratic equation ax² + bx + c = 0 in vertex form a(x − h)² + k = 0 and, when possible, solve for x. You enter coefficients a, b, and c, click Get result, and the tool shows the completed square form, any real solutions, and each algebraic step used. It is designed for students, teachers, and anyone reviewing algebra, and runs entirely in your browser with no sign-up or installation.
Completing the square is a classic method for solving quadratic equations and understanding their graphs. After dividing by a (if needed), you add and subtract (b/2)² to create a perfect square trinomial. The left side factors into (x + b/2)², and the constant terms move to the right side. From there, you can take the square root of both sides and solve for x. This calculator follows exactly that procedure and lists the steps so you can see how each transformation works.
Vertex form a(x − h)² + k reveals the vertex of the parabola at (h, k), which is the maximum or minimum point of the quadratic function. That makes completing the square useful for graphing, optimization problems, and applied questions in physics, finance, and geometry. For example, you can use vertex form to find the peak height of a projectile or the optimal value in a cost or profit function. Understanding the method also helps you see where the quadratic formula comes from.
Use this calculator to practice the method, check homework, or quickly convert equations to vertex form. It is mobile-friendly and works well on phones, tablets, and laptops. For equations you want to solve directly with the quadratic formula or by factoring, you can pair this page with our other algebra tools. Completing the square gives deeper insight into how quadratics behave, making it a valuable technique for any algebra student.