Solve Quadratic Equation by Completing the Square Worksheets


Related Topics:
More Math Worksheets




Share this page to Google Classroom

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)

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 π‘₯. 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:

π‘Žπ‘₯2 + 𝑏π‘₯ + 𝑐 = 0

  1. Move the constant term to the other side of the equation:
    Rewrite it as: π‘Žπ‘₯2 + 𝑏π‘₯ = βˆ’π‘
  2. Make the coefficient of π‘₯2 equal to 1:
    If π‘Ž β‰  1, divide every term by π‘Ž.
  3. Complete the square:
    Take half of the coefficient of π‘₯, 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 π‘₯ 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.
Solve quadratics by completing the square



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

Solve Quadratic Equation by Completing the Square
Β 

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 β‰  1)
Solve Quadratic Equation by Completing the Square Worksheet #4 (mixed)

Solve Quadratic Equation by Completing the Squares

More Printable Worksheets




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.
Mathway Calculator Widget



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