## Quadratic Equations: Completing the Square

#### Aligned To Common Core Standard:

**High School** - HSA-REI.B.4a

How Do You Complete the Square in Quadratic Equations -
Completing the square is one of the most basic things you'll learn on an intermediate level in mathematics. So, whenever you are asked to find the roots, it means that you have been asked to find the value x where the value of y = 0.
Y = 4x^{2} + 40x + 280, 0 = 4x^{2} + 40x + 280
The first step needs to be about making the equation simpler so that it is easier to solve. If we divide both sides by 4, we get:
x^{2} + 10x + 70
Now time to make a perfect square. Here you can create assumptions. We can add and subtract terms as well.
For example:
x^{2} + 10x + 25 - 25 + 70, 0 = (x + 5)^{2} + 45
Subtracting 45 on both sides,
- 45 = (x + 5)^{2} + 45 - 45, √- 45 = (x + 5)^{2}
There are no roots possible for the above equation as the root is in minus and therefore means no real number will exists for the value of x. Students can use these worksheets and lesson to learn how to solve quadratic equations by rearranging the equation, in such a way, that the left side of the equation is a perfect square trinomial.

### Printable Worksheets And Lessons

- Complete the Polynomial
Step-by-step Lesson- Find the missing part of the polynomial
to make a square.

- Guided Lesson
- Find all the endings of these polynomials. Once you try one, you
will get the rest of them.

- Guided Lesson Explanation
- You can do all these in two simple steps.

- Practice Worksheet
- The page should provide more than enough room to save you from
needing scrap paper.

- Factoring the Difference
of Two Perfect Squares Worksheet Five Pack - Factor away at
all of these squares.

- Matching Worksheet
- Match the polynomials to their missing parts.

- Factoring Polynomials Five
Worksheet Pack - Factor the polynomials that you are given down
to their least form.

#### Homework Sheets

I remember saying that this was a great skill when the Common Core first introduced it.

- Homework 1 - Complete the square and fill in the number that makes the polynomial a perfect-square quadratic.
- Homework 2 - Find the best method you can use to complete the square.
- Homework 3 - Perfect square quadratic polynomials follow the standard form of: a^2+ bx + c

#### Practice Worksheets

I find that students really start the grasp the nature of what a quadratic equation really is with this skill.

- Practice 1 - Complete the square by writing the value that makes the polynomial a perfect-square quadratic.
- Practice 2 - What is missing from this picture? Make each value a perfect-square quadratic.
- Practice 3 - The constant is what we do not have. See what fits best based on what you have learned.

#### Math Skill Quizzes

I mixed up the way the problem is stated in a number of different ways.

- Quiz 1 - Factor the following quadratics and cover all the skills that we have learned so far.
- Quiz 2 - Get this done, the way it can be done. We are dealing with much larger values that will take more time.
- Quiz 3 - Some factors are simple, others require some thought. This is a fair sample of all the problem types we have covered.

### When Do You Use the "Completing the Square" Method?

As we have discussed on our previous topic page there are several different methods you can use to solve quadratics. When do you use the method that we are exploring here? The overall answer is that it depends on what you are trying to grasp about the quadratic. In most cases we use this method to determine the roots of the equation. This is because this method does not have a need to use rational factors. If you are looking for complex roots, this is your go to technique. If the quadratic present itself in proper form or you can easily manipulate it to be in proper form (a^{2} + 2ab + b^{2}), then it is already square. This method can be used rearrange an equation to make it easier to work with. As you move on to advance quadratics, this method will simply be used to help you rearrange equations to make the math easier to work with. Who doesn't want to work on something that is less complex?