These lessons, with videos, examples and step-by-step solutions, help Algebra and Grade 9 students learn about solving quadratic equations by completing the square.

**Related Pages**

Factoring Out Common Factors (GCF)

More Lessons for Grade 9 Math

Math Worksheets

**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

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