Completing the Square Formula

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Completing the square formula is a very useful tool that converts quadratic equation into number with x

squared equal to a number. We use this technique of completing the square to rearrange the quadratic into

square equals a number format. This method of completing the square formula helps to simplify algebraic

terms. For completing the square formula is done in number of steps. The following examples of completing

the square formula with help to understand this better.


Example 1: Simplify using completing the square formula for the equation 4x^2 – 2x - 5


Solution: The steps to solve this equation are as follows:

 4x^2 – 2x – 5 = 0; 4x^2 -2x = 5

 x^2 – 1/2x = 5/4 (divide all the terms by 4)

 x^2 – ½ x + 1/16 = 5/4 + 1/16 (add square of half the coefficient of x term)

 (x – ¼)^2 = 21/16

 This way we have the x term squared. To solve for x just square root both the sides

 X – ¼ = √21/4; X = +-√21/4 + ¼

 X = ¼ - √21/4 and x = ¼ + √21/4

 
Example 2: Simplify using completing the square formula for the equation x^2 + 6x - 7


Solution: The steps to solve this equation are as follows:

 x^2 + 6x – 7 = 0; x^2 - 6x = 7

 x^2 + 6x + 9 = 5/4 + 9 (add square of half the coefficient of x term)

 (x + 3)^2 = 16

 This way we have the x term squared. To solve for x just square root both the sides

 X + 3 = +- 4

 X = 1 and x = -7

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