SOLVING LINEAR AND QUADRATIC EQUATIONS

Square Root Method - All quadratic equations can be solved by this method. However, we might
want to avoid this method for some quadratic equations because it can get very cumbersome.

 •Isolate the squared term on one side of the equation. Be sure its coefficient is a positive 1 !!!!!!
 •Apply the Square Root Property.
 •If necessary, further isolate the variable.

Following are two examples for which the Square Root Methods works well:

Example 1:

Solve . Find real solutions only!

Isolate the squared term

and use the Square Root Property

or

The real solutions are

Example 2:

Solve . Find real solutions only!

Isolate the squared term

use the Square Root Property

and further isolate the variable

Simplify the radical

or

There are NO real solutions.

Example 3:

Solve . Find real solutions only!

Let's use the Square Completion Method to help us solve the equation by the Square
Root Method.

Notice that our equation has three terms, but it is not a Perfect Square Trinomial. We will
use for our Perfect Square Trinomial. The middle term is .

Procedure

1. Divide the coefficient of the middle term by 2:

2. Raise to the second power: . We have just found the third term
of the Perfect Square Trinomial!

3. Insert the third term into the given equation, however, in order not to
CHANGE THE VALUE OF THE EQUATION we also have to subtract the
inserted value as follows:

4. Lastly, we factor:

Now we can solve the equation using the Square Root Method as follows:

The real solutions are