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

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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)

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Solve Quadratic Equation by Completing the Squares

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