x² + 8x + 7 = 0
Show answer
(x + 4)² = 9; x = −1 or −7
Free printable worksheet
Completing the Square Worksheet
Fourteen problems solving quadratic equations and rewriting quadratics in vertex form.
Algebra 1Grades 8-114 pagesAnswer key included
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What this worksheet includes
- Fourteen problems solving quadratic equations and rewriting quadratics in vertex form.
- 4-page printable PDF with a complete answer key
- Designed for Grades 8-11 algebra 1 practice
- Available as an immediate free download with no email required
How to use it
Use this completing the square worksheet for guided practice, independent review, homework, tutoring sessions, or a quick skills check. The spacious layout is designed to leave room for students to show their work rather than guess from crowded answer choices.
After students finish, compare their reasoning with the included answer key. When an answer is incorrect, have the student locate the first step where their work changed direction before trying the problem again.
Who this practice is for
This resource is designed for grades 8-11 students working on algebra 1. Teachers, tutors, homeschool families, and parents can preview the first page before deciding whether the level and spacing fit the student.
Looking for a broader sequence? Browse all Algebra I worksheets.
Topic guide
How to approach completing the square
Completing the square turns x² + bx into a perfect-square trinomial by adding (b ÷ 2)². When solving an equation, that value must be added to both sides to preserve equality.
The method also rewrites quadratics in vertex form, making the vertex and axis of symmetry visible. Keep the coefficient of x² equal to 1 inside the completing-square step.
Learning objectives
- Create a perfect-square trinomial
- Solve quadratics by taking square roots
- Rewrite quadratics in vertex form
Skills to review first
- Perfect-square binomials
- Balancing equations
- Square roots and plus-or-minus
Worked example
Follow the reasoning step by step
Solve x² + 6x − 7 = 0 by completing the square.
- Move the constant: x² + 6x = 7.
- Add (6 ÷ 2)² = 9 to both sides.
- Factor: (x + 3)² = 16.
- Take square roots: x + 3 = ±4.
Solution: x = 1 or x = −7.
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
x² − 10x + 21 = 0
Show answer
(x − 5)² = 4; x = 3 or 7
x² + 4x − 1 = 0
Show answer
(x + 2)² = 5; x = −2 ± √5
Error check
Common mistakes to watch for
- Adding b² instead of (b ÷ 2)²
- Adding a value to only one side
- Forgetting both square-root solutions