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More Lessons for Grade 9 Math

Math Worksheets

Videos, worksheets, solutions, and activities to help Algebra and Grade 9 students learn about solving quadratic equations by completing the square.

**Completing The Square**

How to complete the square of a quadratic equation where the coefficient of x squared is equal to one or greater than one?

Step 1. Write the quadratic in the form

ax^{2} + bx + ____ = c + ____

Step 2. If a ≠ 1, divide both sides of the equations by a

Step 3. Add (b/2)^{2} to both sides of the equation

Step 4. Factor the left side of the equation. It should be a perfect square trinomial. Write it as a binomial squared.

Step 5. Square root both sides of the equation and solve for x.

Example:

Solve by completing the square

3x^{2} - 7x - 2 = 0

Completing The Square - Algebra Help

Students learn to solve quadratic equations by completing the square.

Example:

m^{2} + 12m + 30 = 0

**Completing the Square - Solving Quadratic Equations**

This video shows a slightly harder example of completing the square to solve a quadratic equation.

Example:

Solve 2x^{2} - 6x + 3 = 0
**Advanced Completing the Square**

Students learn to solve advanced quadratic equations by completing the square. Note that the quadratic equations in this lesson have a coefficient on the squared term, so the first step is to get rid of the coefficient on the squared term by dividing both sides of the equation by this coefficient.

Example:

3n^{2} - 4n - 1 = 0

**Completing the Square - Leading Coefficient Not 1 (complex solutions)**

How to solve a quadratic equation by completing the square when the leading coefficient is not equal to 1 and the solutions are complex?

Example:

Solve by completing the square

3x^{2} - 4x - 2 = 0

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Grade 9 Math

Math Worksheets

Videos, worksheets, solutions, and activities to help Algebra and Grade 9 students learn about solving quadratic equations by completing the square.

How to complete the square of a quadratic equation where the coefficient of x squared is equal to one or greater than one?

Step 1. Write the quadratic in the form

ax

Step 2. If a ≠ 1, divide both sides of the equations by a

Step 3. Add (b/2)

Step 4. Factor the left side of the equation. It should be a perfect square trinomial. Write it as a binomial squared.

Step 5. Square root both sides of the equation and solve for x.

Example:

Solve by completing the square

3x

Completing The Square - Algebra Help

Students learn to solve quadratic equations by completing the square.

Example:

m

This video shows a slightly harder example of completing the square to solve a quadratic equation.

Example:

Solve 2x

Students learn to solve advanced quadratic equations by completing the square. Note that the quadratic equations in this lesson have a coefficient on the squared term, so the first step is to get rid of the coefficient on the squared term by dividing both sides of the equation by this coefficient.

Example:

3n

How to solve a quadratic equation by completing the square when the leading coefficient is not equal to 1 and the solutions are complex?

Example:

Solve by completing the square

3x

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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