Lesson Worksheet: Solving Quadratic Equations by Completing a Square Mathematics

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

Q1:

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

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

Q2:

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

  • A254
  • B814
  • C9
  • D92
  • E−814

Q3:

Write the equation 𝑥+6𝑥−3=0 in completed square form.

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

Q4:

Complete the square for the expression 𝑥+6𝑥+20.

  • A(𝑥+6)−16
  • B(𝑥+3)+11
  • C(𝑥+3)+20
  • D(𝑥−3)+11
  • E(𝑥−6)−16

Q5:

Complete the square for the expression 𝑥+12𝑥.

  • A(𝑥−6)+12
  • B(𝑥−6)+36
  • C(𝑥+6)+36
  • D(𝑥+6)−36
  • E(𝑥+6)−12

Q6:

Given that 𝑥−10𝑥=(𝑥+𝑝)+𝑞, what are the values of 𝑝 and 𝑞?

  • A𝑝=−5, 𝑞=−25
  • B𝑝=−10, 𝑞=−100
  • C𝑝=5, 𝑞=−25
  • D𝑝=−5, 𝑞=25
  • E𝑝=10, 𝑞=−100

Q7:

Given that 𝑥+2𝑥+5=(𝑥+𝑝)+𝑞, what are the values of 𝑝 and 𝑞?

  • A𝑝=2, 𝑞=5
  • B𝑝=1, 𝑞=4
  • C𝑝=5, 𝑞=1
  • D𝑝=1, 𝑞=5
  • E𝑝=2, 𝑞=1

Q8:

In completing the square for quadratic function 𝑓(𝑥)=𝑥+14𝑥+46, you arrive at the expression (𝑥−𝑏)+𝑐. What is the value of 𝑐?

Q9:

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

Q10:

Solve the equation 𝑥−14𝑥+38=0 by completing the square.

  • A𝑥=−4 or 𝑥=18
  • B𝑥=11+√7 or 𝑥=11−√7
  • C𝑥=7 or 𝑥=11
  • D𝑥=7+√11 or 𝑥=7−√11
  • E𝑥=18 or 𝑥=−18

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