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Lesson: Solving Quadratic Equations 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

00:45
02:30

Worksheet • 14 Questions • 2 Videos

Q1:

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

Q2:

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

Q3:

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
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