Complete the Square Calculator

Enter \(ax^2+bx+c\) (integers, decimals, fractions). Each step includes an explanation right next to the algebra. Final vertex form is simplified.

⧉ complete the square

ax² + bx + c → a(x + h)² + k
coefficients

Step‑by‑step (explanation inside)

Vertex form: \(2(x+1.5)^2 -2\)
Vertex: \((-1.5, -2)\)
Entered: \(2x^2+6x+\frac{5}{2}\)

Method summary

\(h = \dfrac{b}{2a},\; k = c - a h^2\)   →   \(a(x+h)^2 + k\)     Vertex \((-h, k)\)

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