Completing the Square Practice Worksheet
Practice rewriting quadratics and solving equations by completing the square with step-by-step solutions.
Try each problem first. Then click Show solution to check your work. Completing the square is all about creating a perfect square trinomial.
Key Idea
For an expression like \(x^2 + bx\), add:
Level 1: Build the Perfect Square
Problem 1
Complete the square:
Show solution
Take half of \(6\), then square it.
Add \(9\) to make a perfect square trinomial.
Problem 2
Complete the square:
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Take half of \(-10\), then square it.
Add \(25\) to make a perfect square trinomial.
Problem 3
Complete the square:
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Take half of \(14\), then square it.
Level 2: Solve by Completing the Square
Problem 4
Solve:
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Complete the square by adding \(9\) to both sides.
Take the square root of both sides.
Problem 5
Solve:
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Half of \(-8\) is \(-4\), and \((-4)^2=16\).
Take the square root.
Problem 6
Solve:
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Half of \(4\) is \(2\), and \(2^2=4\).
Level 3: Standard Form Quadratics
Problem 7
Solve:
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Move the constant to the other side.
Half of \(10\) is \(5\), and \(5^2=25\).
Problem 8
Solve:
Show solution
Move the constant to the other side.
Half of \(-12\) is \(-6\), and \((-6)^2=36\).
Need more help with completing the square?
Completing the square is easier when you understand why \(\left(\frac{b}{2}\right)^2\) creates a perfect square. For a full explanation, visit my completing the square guide.