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Completing the Square

Related Topics:
Factoring Out Common Factors (GCF).
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 x2 is 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.


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


x² + 6x + 4 = 0

x² + 6x = –4

x² + 6x + 32 = –4 + 32

(x + 3)² = 5

(x + 3) = or (x + 3) = –

x = – 3 or x = – – 3

x = – 3 or x = – – 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.

Completing the Square - Solving Quadratic Equations.


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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