# Completing the square

From Conservapedia

**Completing the square** is a method for solving for the roots of the general quadratic equation:

, where

It is first taught using equations with "friendly" numbers in place of *a*, *b*, and *c* to get the student used to the process.

- What one does is add and multiply by various carefully chosen constants to create an equation of the form:

- where
*d*,*e*and*f*are constants expressed in*a*,*b*, and*c*.

- This resolves to:

- (grouping)
- (take square root)
- (subtract e)
- (divide by e)

By then applying the process to the general equation, we can derive the quadratic formula:

- (given)

- (multiply by 4a)

- (subtract 4ac)

- (add b^2)

- (group each side)

- (take square root, allow for both roots)

- (subtract b)

- (divide by 2a)

We can now determine the real or imaginary roots of any quadratic equation by simply inserting *a*, *b*, and *c* into the formula.