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Lesson: Solving Quadratics by Completing the Square

In this lesson, we will learn how to solve quadratics by completing the square and how to complete the square then solve the equation using inverses.

Video

17:59

Sample Question Videos

02:30
04:16

Worksheet • 13 Questions • 2 Videos

Q1:

Solve the equation π‘₯ βˆ’ 1 4 π‘₯ + 3 8 = 0 2 by completing the square.

  • A π‘₯ = 7 + √ 1 1 or π‘₯ = 7 βˆ’ √ 1 1
  • B π‘₯ = 7 or π‘₯ = 1 1
  • C π‘₯ = 1 1 + √ 7 or π‘₯ = 1 1 βˆ’ √ 7
  • D π‘₯ = 1 8 or π‘₯ = βˆ’ 1 8
  • E π‘₯ = βˆ’ 4 or π‘₯ = 1 8

Q2:

By completing the square, solve the equation π‘₯ βˆ’ 2 √ 3 π‘₯ + 1 = 0 2 .

  • A π‘₯ = √ 3 + √ 2 , π‘₯ = √ 3 βˆ’ √ 2
  • B π‘₯ =  βˆ’ 1 + 2 √ 3 , π‘₯ = βˆ’  βˆ’ 1 + 2 √ 3
  • C π‘₯ = 2 √ 3 , π‘₯ = βˆ’ 2 √ 3
  • D π‘₯ = 1 , π‘₯ = βˆ’ 1
  • E π‘₯ = √ 3 6 , π‘₯ = βˆ’ √ 3 6

Q3:

By completing the square, solve the equation π‘₯ βˆ’ π‘₯ = 3 4 2 .

  • A π‘₯ = 3 2 , π‘₯ = βˆ’ 1 2
  • B π‘₯ = βˆ’ 1 2
  • C π‘₯ = √ 3 2
  • D π‘₯ = 3 4 , π‘₯ = βˆ’ 1 2
  • E π‘₯ = βˆ’ 3 2 , π‘₯ = 1 2

Q4:

By completing the square, solve the equation 1 + π‘₯ = π‘₯ 2 .

  • A π‘₯ = √ 5 + 1 2 , π‘₯ = βˆ’ √ 5 βˆ’ 1 2
  • B π‘₯ = 1 2 , π‘₯ = βˆ’ 1 2
  • C π‘₯ = √ 5 + 1 2
  • D π‘₯ = 1 , π‘₯ = βˆ’ 1
  • E π‘₯ = √ βˆ’ 5 βˆ’ 1 2 , π‘₯ = √ 5 βˆ’ 1 2

Q5:

By completing the square, solve the equation π‘₯ = π‘₯ + 3 4 2 .

  • A π‘₯ = 3 2 , π‘₯ = βˆ’ 1 2
  • B π‘₯ = βˆ’ 1 2
  • C π‘₯ = √ 3 2
  • D π‘₯ = 3 4 , π‘₯ = βˆ’ 1 2
  • E π‘₯ = βˆ’ 3 2 , π‘₯ = 1 2

Q6:

By completing the square, write all of the solutions to π‘₯ βˆ’ 4 π‘₯ + 1 = 0 2 .

  • A 2 + √ 3 , 2 βˆ’ √ 3
  • B5
  • C 2 + √ 3
  • D3
  • E 2 βˆ’ √ 3

Q7:

By completing the square, solve the equation 3 π‘₯ βˆ’ 2 π‘₯ = 2 2 .

  • A π‘₯ = 1 3 + √ 7 3 , π‘₯ = 1 3 βˆ’ √ 7 3
  • B π‘₯ = 4 3 , π‘₯ = βˆ’ 4 3
  • C π‘₯ = 1 3 + √ 7 3
  • D π‘₯ = βˆ’ 1 3 + √ 7 3 , π‘₯ = βˆ’ 1 3 βˆ’ √ 7 3
  • E π‘₯ = 1 3 + √ 5 3 𝑖 , π‘₯ = 1 3 βˆ’ √ 5 3 𝑖

Q8:

By completing the square, write all of the solutions to π‘₯ + 4 π‘₯ + 1 = 0 2 .

  • A βˆ’ 2 + √ 3 , βˆ’ 2 βˆ’ √ 3
  • B βˆ’ 2 + √ 1 2 , βˆ’ 2 βˆ’ √ 1 2
  • C βˆ’ 2 + √ 3
  • D βˆ’ 2
  • E βˆ’ 2 βˆ’ √ 3

Q9:

Solve the equation π‘₯ + 2 2 π‘₯ + 1 1 4 = 0 2 by completing the square.

  • A π‘₯ = βˆ’ 1 1 + √ 7 or π‘₯ = βˆ’ 1 1 βˆ’ √ 7
  • B π‘₯ = βˆ’ 1 1 or π‘₯ = 7
  • C π‘₯ = 7 + √ 1 1 or π‘₯ = 7 βˆ’ √ 1 1
  • D π‘₯ = 4 or π‘₯ = βˆ’ 4
  • E π‘₯ = βˆ’ 1 8 or π‘₯ = βˆ’ 4

Q10:

Solve the equation π‘₯ βˆ’ 1 4 π‘₯ + 4 4 = 0 2 by completing the square.

  • A π‘₯ = 7 + √ 5 or π‘₯ = 7 βˆ’ √ 5
  • B π‘₯ = 7 or π‘₯ = 5
  • C π‘₯ = 5 + √ 7 or π‘₯ = 5 βˆ’ √ 7
  • D π‘₯ = 1 2 or π‘₯ = βˆ’ 1 2
  • E π‘₯ = 2 or π‘₯ = 1 2

Q11:

Solve the equation π‘₯ βˆ’ 2 0 π‘₯ + 7 7 = 0 2 by completing the square.

  • A π‘₯ = 1 0 + √ 2 3 or π‘₯ = 1 0 βˆ’ √ 2 3
  • B π‘₯ = 1 0 or π‘₯ = 2 3
  • C π‘₯ = 2 3 + √ 1 0 or π‘₯ = 2 3 βˆ’ √ 1 0
  • D π‘₯ = 3 3 or π‘₯ = βˆ’ 3 3
  • E π‘₯ = βˆ’ 1 3 or π‘₯ = 3 3

Q12:

Solve the equation π‘₯ βˆ’ 4 π‘₯ βˆ’ 1 = 0 2 by completing the square.

  • A π‘₯ = 2 + √ 5 or π‘₯ = 2 βˆ’ √ 5
  • B π‘₯ = 2 or π‘₯ = 5
  • C π‘₯ = 5 + √ 2 or π‘₯ = 5 βˆ’ √ 2
  • D π‘₯ = 7 or π‘₯ = βˆ’ 7
  • E π‘₯ = βˆ’ 3 or π‘₯ = 7

Q13:

Solve the equation π‘₯ + 4 π‘₯ + 1 = 0 2 by completing the square.

  • A π‘₯ = βˆ’ 2 + √ 3 or π‘₯ = βˆ’ 2 βˆ’ √ 3
  • B π‘₯ = βˆ’ 2 or π‘₯ = 3
  • C π‘₯ = 3 + √ 2 or π‘₯ = 3 βˆ’ √ 2
  • D π‘₯ = 1 or π‘₯ = βˆ’ 1
  • E π‘₯ = βˆ’ 5 or π‘₯ = 1
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