Grade 9 · Math · Algebra 1

9th grade Complete the square, and solve by completing the square worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Complete the square, and solve by completing the square

Grade 9 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

Milo arranges tiles for x² + 10x: one x-by-x square plus 10 thin strips, split along two sides. What number fills the corner, so x² + 10x + ? is a perfect square?
Noah plans a square quilt from x² + 16x: one big patch plus strips along two sides. What number fills the corner, so x² + 16x + ? is a perfect square?
Pia draws x² - 6x as a square on paper, with a corner left empty. What number fills the corner, so x² - 6x + ? is a perfect square?
Ren's square rug design is x² - 20x, with one corner still missing. What number fills the corner, so x² - 20x + ? is a perfect square?
5.
Tala builds x² + 12x + 36 from algebra tiles. Which shows it written as a perfect square?
- (x + 6)(x - 6)
- (x + 6)²
- (x + 12)²
- (x - 6)²
6.
Zee's puzzle card shows x² - 18x + 81. Which shows it written as a perfect square?
- (x - 9)²
- (x - 9)(x + 9)
- (x + 9)²
- (x - 18)²
7.
Ari sews a square quilt modeled by x² + 22x + 121. Which shows it written as a perfect square?
- (x + 11)(x - 11)
- (x + 22)²
- (x - 11)²
- (x + 11)²
Esme solves x² + 6x = 7 by completing the square. The same number goes on both sides, so the left becomes (x + 3)². What number is on the right?
Jun works on x² + 10x = 11 with a sharp pencil. The same number goes on both sides, so the left becomes (x + 5)². What number is on the right?
Kira solves x² - 4x = 12 with algebra tiles. The same number goes on both sides, so the left becomes (x - 2)². What number is on the right?

Complete the square, and solve by completing the square. Every version has 10 questions, and the answer key prints on the second page.

Standard: A-REI.B.4a, A-SSE.B.3b

complete the square: Add the corner number so the expression is a bracket squared.

corner: The small square (half of the x number, squared) that fills the gap.

perfect square: A bracket times itself, like (x + 5)².

vertex form: a(x - h)² + k: the lowest (or highest) row of the table.

both sides: Whatever is added on the left is added on the right.

Your child added half of the x number instead of half of it squared.

Your child squared the whole x number instead of half of it.

Your child put the whole x number in the bracket.

Ask: if each strip is 5 wide, how big is the corner square?

Ask: the 10x is split into two strips; how wide is each?

Ask: what is (x + 12)² multiplied out?

What is the most common mistake with complete the square, and solve by completing the square?

Your child added half of the x number instead of half of it squared.

How can I help my child with complete the square, and solve by completing the square?

Ask: if each strip is 5 wide, how big is the corner square?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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