NAME:_______________________________________________
Algebra 2 – Lesson 6-2: Solving Quadratics by Completing the Square
DATE:_______
PERIOD:_____
Learning Goals:
1) How do we solve a quadratic equation by completing the square?
DO NOW: Answer the following questions in order to prepare for today’s lesson
1. Solve
by using the square root method.
2. Factor the following trinomials. What do you notice about all of the factors?

Completing the Square

The four expressions above are examples of perfect square trinomials because their factors equal
.
Sometimes you need to add a term to an expression
to make it a perfect square trinomial.
This process is called completing the square.

To complete the square for the expression
, add ( )
PRACTICE: Find the value of c that makes the expression a perfect square trinomial. Then write the
expression as the square of a binomial.
 STEPS TO COMPLETING THE SQUARE
1. The “a” coefficient must equal 1 (divide all terms by “a”)
2. Isolate the x-terms (move “c” to the other side)
3. Take ( ) and add that number to each side
4. Factor the perfect square trinomial and express it as
5. Solve for x by using the square root method
 Completing the Square when
Example 1: Solve
Example 2: Solve
by completing the square, and express the result in simplest form.
by completing the square, and express the results in simplest form.
 STEPS TO COMPLETING THE SQUARE
1. The “a” coefficient must equal 1 (divide all terms by “a”)
2. Isolate the x-terms (move “c” to the other side)
3. Take ( ) and add that number to each side
4. Factor the perfect square trinomial and express it as
5. Solve for x by using the square root method
 Completing the Square when
Example 1: Solve
form.
by completing the square, and express the results in simplest
Example 2: Solve
by completing the square, and express the results in simplest form.
PRACTICE: Solve the following equations by completing the square and express the results in simplest form.
b.
a.
ERROR ANALYSIS: Describe and correct the error in solving the equation below.
√
√