Solve Quadratic Equation by Completing the Square Worksheets

Printable “Quadratic Equations” worksheets:
Solve Quadratic Equation (use factoring)
Solve Word Problems using Quadratic Equations
Sketching Quadratic Graphs

Rewrite Expressions in Completed-Squared Form
Solve Quadratic Equation (use completing the square)
Solve Quadratic Equation (use quadratic formula)
Discriminant in the Quadratic Formula

Examples, solutions, videos, and worksheets to help Algebra 1 students learn how to solve complex quadratic equations, including those with a leading coefficient other than 1, by completing the square. Some solutions may be irrational.

How to solve equations by completing the square?

To solve a quadratic equation by completing the square, we use the method of completing the square to rewrite the equation in a form where we can isolate 𝑥. Here’s a step-by-step guide along with an example.

Steps to Solve a Quadratic Equation by Completing the Square
Given an equation of the form:

𝑎𝑥² + 𝑏𝑥 + 𝑐 = 0

1. Move the constant term to the other side of the equation:
   Rewrite it as: 𝑎𝑥² + 𝑏𝑥 = −𝑐
   
2. Make the coefficient of 𝑥² equal to 1:
   If 𝑎 ≠ 1, divide every term by 𝑎.
   
3. Complete the square:
   Take half of the coefficient of 𝑥, square it, and add this value to both sides of the equation.
   
4. Rewrite as a perfect square on the left side.
   
5. Solve for 𝑥 by isolating it and taking the square root of both sides.
   

The following example shows how to solve a quadratic equation by completing the square.

Have a look at this video if you need to review how to solve quadratic equations by completing the square.

• Solve Quadratic Equation by Completing the Square

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more Solve Quadratic Equation by Completing the Square Worksheets.

 

More Solve Quadratic Equation by Completing the Square Worksheets

Printable
(Answers on the second page.)
Solve Quadratic Equation by Completing the Square Worksheet #1 (a = 1, b is even)
Solve Quadratic Equation by Completing the Square Worksheet #2 (a = 1)
Solve Quadratic Equation by Completing the Square Worksheet #3 (a ≠ 1)
Solve Quadratic Equation by Completing the Square Worksheet #4 (mixed)

Related Lessons & Worksheets

Solve Quadratic Equation by Completing the Squares

More Printable Worksheets

Check out our most popular games!

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.