This document provides 4 examples of solving quadratic equations by completing the square, where each example has a different combination of positive or negative coefficients for the squared term and values of a and c, resulting in solutions with rational or irrational roots of various signs.

1. Completing the Square

2. Overview
This set of tutorials provides 4 examples of solving
quadratic equations by completing the square.
The algorithm below shows how to complete the
square using the values for a and c as shown.

3. In this Example the squared term has a negative coefficient, while the
values for a and c are positive. The solution has two rational numbers, one
positive and one negative. Each root simplifies to an integer value.

4. In this Example the squared term has a positive coefficient, while the
values for a and c are negative. The solution has two rational numbers,
one positive and one negative. Each root simplifies to an integer value.

5. In this Example the squared term has a negative coefficient, while
the values for a and c are positive. The solution has two irrational
numbers, one positive and one negative.

6. In this Example the squared term has a postive coefficient, while
the values for a and c are positive. The solution has two irrational
numbers, both negative.

7. In this Example the squared term has a postive coefficient, while
the values for a and c are positive. The solution has two irrational
numbers, both negative.