🔳Completing the Square Calculator
Convert ax² + bx + c to vertex form a(x − h)² + k with every step shown.
Free Completing the Square Calculator
Completing the square is one of the trickier algebra techniques to follow by hand. Our free completing the square calculator takes any quadratic ax² + bx + c and converts it to vertex form a(x − h)² + k, showing every algebraic step along the way.
Enter your coefficients and watch the process unfold: factoring out the leading coefficient, halving and squaring the linear term, and rewriting the expression as a perfect square plus a constant. From there, the calculator derives the vertex, the axis of symmetry, and the roots — cross-checked against the quadratic formula.
Cases with no real roots are explained clearly rather than shown as an error, and coefficients are handled exactly, including clean fractions rather than rounded decimals. No sign-up, no downloads, no limits.