A Completing the Square Calculator helps solve quadratic equations and second-degree polynomials in the form

ax² + bx + c = 0, where a ≠ 0

This method is especially useful when factoring isn’t possible, making it a reliable tool for both real and complex solutions.

What is Completing the Square?

Completing the square involves transforming the left side of a quadratic equation into a perfect square binomial. It allows us to solve the equation systematically, even when factoring isn’t an option.

How to Complete the Square:

1. Rearrange the equation to the form ( ax^2 + bx + c = 0 ).
2. If ( a != 1 ), divide the equation by ( a ).
3. Move the constant ( c ) to the right side.
4. Take ( b ), divide by 2, and square it. Add this value to both sides.
5. Rewrite the left side as a perfect square binomial.
6. Take the square root of both sides.
7. Solve for ( x ), noting you will have two solutions.

Using this calculator, you can automate this process and quickly solve quadratic equations with real or complex solutions.