Allday Education

Free Completing the Square Worksheet

Ten completing-the-square problems with a worked answer key.

Answer key included
Name: Date:
Completing the Square
1.
x2+2x2x^2 + 2x - 2
2.
x22x7x^2 - 2x - 7
3.
x24x3x^2 - 4x - 3
4.
x2+6x9x^2 + 6x - 9
5.
x2+6x2x^2 + 6x - 2
6.
x2+10x+2x^2 + 10x + 2
7.
x2+10x+1x^2 + 10x + 1
8.
x212x5x^2 - 12x - 5
9.
x2+2x6x^2 + 2x - 6
10.
x212x+6x^2 - 12x + 6
Andy · alldayeverydaymath.com
Name: Answer KeyDate:
Completing the Square
1.
x2+2x2x^2 + 2x - 2
Answer: (x+1)23(x + 1)^2 - 3
2.
x22x7x^2 - 2x - 7
Answer: (x1)28(x - 1)^2 - 8
3.
x24x3x^2 - 4x - 3
Answer: (x2)27(x - 2)^2 - 7
4.
x2+6x9x^2 + 6x - 9
Answer: (x+3)218(x + 3)^2 - 18
5.
x2+6x2x^2 + 6x - 2
Answer: (x+3)211(x + 3)^2 - 11
6.
x2+10x+2x^2 + 10x + 2
Answer: (x+5)223(x + 5)^2 - 23
7.
x2+10x+1x^2 + 10x + 1
Answer: (x+5)224(x + 5)^2 - 24
8.
x212x5x^2 - 12x - 5
Answer: (x6)241(x - 6)^2 - 41
9.
x2+2x6x^2 + 2x - 6
Answer: (x+1)27(x + 1)^2 - 7
10.
x212x+6x^2 - 12x + 6
Answer: (x6)230(x - 6)^2 - 30
Andy · alldayeverydaymath.com

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About this worksheet

Students complete the square to rewrite a quadratic — the move behind the quadratic formula and vertex form. Numbers keep the perfect-square step clean so the method stays visible.

Focus on the coefficient of the linear term: halve it, then square that half. When rewriting an expression, adding that square must be balanced by subtracting it so the expression keeps the same value.

Students shaky on the skill itself? Send them to the free lesson: Completing the Square — explained step by step.

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