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## Quadratic Equations: Completing the Square

#### 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 = 4x2 + 40x + 280, 0 = 4x2 + 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: x2 + 10x + 70 Now time to make a perfect square. Here you can create assumptions. We can add and subtract terms as well. For example: x2 + 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  #### 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.