# Completing the Square Calculator

## Calculator Use

This calculator is a **quadratic equation solver** that will solve a second-order polynomial equation in the form ax^{2} + bx + c = 0 for x, where a ≠ 0, using the **completing the square method**.

The calculator solution will show work to solve a quadratic equation by completing the square to solve the entered equation for real and complex roots.

## Completing the square when a is not 1

To complete the square when a is greater than 1 or less than 1 but not equal to 0, factor out the value of a from all other terms.

For example, find the solution by completing the square for:

\( a \ne 1, a = 2 \) so divide through by 2

which gives us

Now, continue to solve this quadratic equation by completing the square method.

## Completing the square when b = 0

When you do not have an x term because b is 0, you will have a easier equation to solve and only need to solve for the squared term.

For example: Solution by completing the square for:

Eliminate b term with 0 to get:

Keep \( x \) terms on the left and move the constant to the right side by adding it on both sides

Take the square root of both sides

therefore

**Cite this content, page or calculator as:**

Furey, Edward "Completing the Square Calculator"; from *https://www.calculatorsoup.com* - Online Calculator Resource.