Completing the Square

Factoring Quadratic Equations using  Perfect Square Trinomial (Square of a Sum or Square of a Difference) or Difference of Two Squares.

Factoring Quadratic Equations where the coefficient of x²is 1.
Factoring Quadratic Equations where the coefficient of x² is greater than 1 
Factoring Quadratic Equations using the Quadratic Formula.

There are several techniques that can be used to factor quadratic equations.
In this lesson, we will learn how to use Completing the Square method to solve quadratic equations. It involves adding a constant to both sides of the equation in oder to get a squared expression on one side of the equation.

Example:

Find the roots of the equation: x² + 6x + 4 = 0, correct to 3 significant figures.

Solution:

x² + 6x + 4 = 0

x² + 6x = –4

x² + 6x + 3² = –4 + 3²

(x + 3)² = 5

(x + 3) = √5 or (x + 3) = – √5

x = √5 – 3 or x = – √5 – 3

x = √5 – 3 or x = – √5 – 3

x = –0.764 or x = –5.24 (correct to 3 sig. fig.)

The following videos will explain in detail how to solve quadratic equations using completing the square method.

• Show Step-by-step Solutions

• Show Step-by-step Solutions

• Show Step-by-step Solutions

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