How to Calculate Completing the Square - Formula, Example

How to Calculate Completing the Square - Definition

Definition:

Completing the Square is a kind of method which is used to solve the quadratic equations by means of either adding or subtracting terms on both sides of the equation.

Formula:

Step 1 : Move the loose number over to the other side Step 2 : Divide all the terms by a coefficient of x^2. Step 3 : Take half of the coefficient (don't forget the sign!) of the x-term, and square it. Add this square to both sides of the equation. Step 4 : Convert the left-hand side to squared form, and simplify the right-hand side. Step 5 : Solve for x value (Add for x1 and Subtract for x2)

Example:

Solve 4x^2-2x-5 = 0

Solution:

Step 1:

Move the loose number over to the other side So let us move -5 to the right side of the equation,4x^2-2x= 5

Step 2:

Divide all the terms by a coefficient of x^2 (Here, 4 is the coefficient of x^2) x^2-x/2= 5/4

Step 3:

Take half of the coefficient (don't forget the sign!) of the x-term, and square it. Add this square to both sides of the equation. x^2-x/2= 5/4 (-1/2)-> -1/4=1/16 x^2-x/2+1/16= (5/4)+(1/16)

Step 4:

Convert the left-hand side to squared form, and simplify the right-hand side. (x-1/4)^2=21/16 Square-root both sides, remembering the ± on the right-hand side. Simplify as necessary. x-1/4= ± sqrt(21/16)

Step 5:

Solve for x value x=1/4 ± sqrt(21/16) x1=1/4 + sqrt(21)/4 and x2=1/4 - sqrt(21)/4 x1= 1.4 and x2= -0.9

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