Completing the Square Calculator

Completing the square is a method for solving quadratic equations of the form \(ax^2 + bx + c = 0\).

1. Isolate the x terms: Move the constant term \(c\) to the other side of the equation.
2. Divide by a: If \(a \neq 1\), divide every term in the equation by \(a\).
3. Complete the Square: Take half of the new \(b\) coefficient, square it, and add this value to both sides of the equation. The value is \( \left(\frac{b}{2a}\right)^2 \).
4. Factor: The side with the x terms will now be a perfect square trinomial, which can be factored into \( \left(x + \frac{b}{2a}\right)^2 \).
5. Solve for x: Take the square root of both sides (remembering the ±) and solve for \(x\).