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Completing the square worksheets Grade 9

Solve quadratic equations by completing the square.

The front of the free completing the square worksheet
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Free · Worked example · 8 problems · Answer key · US Letter

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How to do it

Move the number over, add (b ÷ 2)² to both sides, write a square, take the square root.

x2−10x+21=0x^{2} - 10x + 21 = 0
x2−10x=−21x^{2} - 10x = -21move the number to the other side
x2−10x+25=−21+25x^{2} - 10x + 25 = -21 + 25add (−10 ÷ 2)² = 25 to both sides
(x−5)2=4(x - 5)^{2} = 4write the left side as a square
x−5=±2x - 5 = \pm 2take the square root of both sides
x=3 or x=7x = 3\ \text{or }x = 7

Example problems

  1. x2+2x=0x^{2} + 2x = 0
  2. x2+2x−2=0x^{2} + 2x - 2 = 0
  3. x2+2x−28=0x^{2} + 2x - 28 = 0
  4. x2−12x+35=0x^{2} - 12x + 35 = 0

Radicals, quadratics and rational expressions

  1. Simplifying square roots
  2. Adding and multiplying radicals
  3. Solving quadratic equations by factoring
  4. Completing the square
  5. The quadratic formula
  6. Simplifying rational expressions
  7. Multiplying and dividing rational expressions