Completing the Square Examples, Definition

Completing the Square examples: Sometimes, the quadratic polynomials are not easily factorable.

For Example, consider x^2+4x-437=0
It is difficult to make factors of x^2+4x-437
In such a case the factorization and hence the solution of a quadratic equation can be found by the method of completing the square and extracting square roots.

Completing the Square examples

Say we have a simple expression like x^2 +bx. Having x  twice in the same expression can make life hard. What can we do?

Well, with a little inspiration from Geometry we can convert it, like this:

Completing the Square Examples

Solve the equation x^2 + 4x - 437 = 0 by completing the square examples).


we have

x^2 + 4x - 437 = 0


Now, for completing the square, adding both side (\frac42)^2







⇒x=21-2 \;\;\;\;\;\;or\;\;\;\;\;\; x=-21-2

so\;\;\;\;\;\; x=19 \;\;\;\;\;\;and \;\;\;\;\;\;x=-23

Hence by completing the square

Solution set={19,-23}


Solve the equation x^2 -2x - 899 = 0 by completing the square examples.


we have

x^2 -2x - 899 = 0


Now, for completing the square, adding both side (\frac22)^2







⇒x=30+1 \;\;\;\;\;\;or\;\;\;\;\;\; x=-30+1

so\;\;\;\;\;\; x=31 \;\;\;\;\;\;and \;\;\;\;\;\;x=-29

Hence by completing the square

Solution set={31.-29}

you can also see quadratic formula

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Azhar Ali

Azhar Ali

I graduated in Mathematics from the University of Sargodha, having master degree in Mathematics.

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