Lesson Worksheet: Solving Quadratics: Completing the Square‎ Mathematics

In this worksheet, we will practice solving quadratics by completing the square.


Solve the equation 𝑥14𝑥+38=0 by completing the square.

  • A𝑥=4 or 𝑥=18
  • B𝑥=11+7 or 𝑥=117
  • C𝑥=7 or 𝑥=11
  • D𝑥=7+11 or 𝑥=711
  • E𝑥=18 or 𝑥=18


By completing the square, solve the equation 𝑥23𝑥+1=0.

  • A𝑥=1+23, 𝑥=1+23
  • B𝑥=1, 𝑥=1
  • C𝑥=3+2, 𝑥=32
  • D𝑥=23, 𝑥=23
  • E𝑥=36, 𝑥=36


By completing the square, solve the equation 𝑥𝑥=34.

  • A𝑥=12
  • B𝑥=32, 𝑥=12
  • C𝑥=32
  • D𝑥=34, 𝑥=12
  • E𝑥=32, 𝑥=12


By completing the square, solve the equation 1+𝑥=𝑥.

  • A𝑥=512, 𝑥=512
  • B𝑥=12, 𝑥=12
  • C𝑥=5+12
  • D𝑥=5+12, 𝑥=512
  • E𝑥=1, 𝑥=1


By completing the square, solve the equation 𝑥=𝑥+34.

  • A𝑥=32
  • B𝑥=12
  • C𝑥=32, 𝑥=12
  • D𝑥=32, 𝑥=12
  • E𝑥=34, 𝑥=12


By completing the square, solve the equation 3𝑥2𝑥=2.

  • A𝑥=43, 𝑥=43
  • B𝑥=13+73, 𝑥=1373
  • C𝑥=13+53𝑖, 𝑥=1353𝑖
  • D𝑥=13+73
  • E𝑥=13+73, 𝑥=1373


Solve the equation 𝑥+22𝑥+114=0 by completing the square.

  • A𝑥=18 or 𝑥=4
  • B𝑥=7+11 or 𝑥=711
  • C𝑥=11 or 𝑥=7
  • D𝑥=11+7 or 𝑥=117
  • E𝑥=4 or 𝑥=4


Solve the equation 𝑥14𝑥+44=0 by completing the square.

  • A𝑥=2 or 𝑥=12
  • B𝑥=5+7 or 𝑥=57
  • C𝑥=7 or 𝑥=5
  • D𝑥=7+5 or 𝑥=75
  • E𝑥=12 or 𝑥=12


Solve the equation 𝑥20𝑥+77=0 by completing the square.

  • A𝑥=13 or 𝑥=33
  • B𝑥=23+10 or 𝑥=2310
  • C𝑥=10 or 𝑥=23
  • D𝑥=10+23 or 𝑥=1023
  • E𝑥=33 or 𝑥=33


Solve the equation 𝑥4𝑥1=0 by completing the square.

  • A𝑥=3 or 𝑥=7
  • B𝑥=5+2 or 𝑥=52
  • C𝑥=2 or 𝑥=5
  • D𝑥=2+5 or 𝑥=25
  • E𝑥=7 or 𝑥=7


Solve the equation 𝑥+4𝑥+1=0 by completing the square.

  • A𝑥=5 or 𝑥=1
  • B𝑥=3+2 or 𝑥=32
  • C𝑥=2 or 𝑥=3
  • D𝑥=2+3 or 𝑥=23
  • E𝑥=1 or 𝑥=1


By completing the square, solve the equation 𝑥+8𝑥10=0.

  • A𝑥=4+26, 𝑥=426
  • B𝑥=264, 𝑥=264
  • C𝑥=4+26, 𝑥=426.
  • D𝑥=26, 𝑥=26
  • E𝑥=426, 𝑥=426


While completing the square, James transformed 𝑥+9𝑥5=0 into 𝑥+9𝑥=5. He then added a number to both sides. What number did he add?

  • A254
  • B814
  • C9
  • D92
  • E814


Write the equation 𝑥+6𝑥3=0 in completed square form.

  • A(𝑥+3)9=0
  • B(𝑥3)9=0
  • C(𝑥3)12=0
  • D(𝑥+6)39=0
  • E(𝑥+3)12=0


Solve 𝑥+3𝑥6=0.

  • A𝑥=3+332 or 𝑥=3332
  • B𝑥=3+33 or 𝑥=333
  • C𝑥=3+332 or 𝑥=3332
  • D𝑥=3+33 or 𝑥=333
  • E𝑥=3+332 or 𝑥=3332

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