# Solve Quadratic Equations by Completing the Square: Examples

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
ax2 + 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
3x2 - 7x - 2 = 0

Completing The Square - Algebra Help
Students learn to solve quadratic equations by completing the square.

Example:
m2 + 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 2x2 - 6x + 3 = 0

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:
3n2 - 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
3x2 - 4x - 2 = 0

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