The Completing the square method - Quadratic Equation

Completing The square method of Quadratic Equation
Another quick way of solving quadratic equation as earlier stated is by using completing the square method .
It is so simple if you had understand how we derived our formular method of the quadratic equation.
Remember quadratic Equations are polynomial of the second degree other and is form can be represented as below:
Ax^2 + Bx+ C =0
Some quadratics are very simple to solve because they come in simple form like below:
Say (x-3)^2=9
This type of quadratic equation could quickly be solved by taking square root of both sides of the equation.
i.e sqrt ( x-3)^2 =sqrt(9)
x-3=+0r-3 (note that when you take a square root of a number say 9 for example,the result would be either + 0r - )
By solving for x in the equation above we going to have two answers.
i.e x=3+3 or x=3-3
x=6 or x=0
But,what about the situation when our equation do not come in this form. Most quadratic equation will not come neatly squared like this. In this case you first use your mathematical technique to arranged the quadratics in a neatly squared part equals to a number like the example treated above. Thus, the completing the square method.

For a typical Example:
Solve the quadratic equation 4x^2 -2x-5=0
Solution
Step 1: move -5 to the R.H.S to the equation (R.H.S-right hand side)
4x^2-2x=5 (remember when you move -5 to the other side of the equation it becomes +5)
Step 2: Divide through by the co efficient of your X squared term (which is 4 in our example)
The equation now becomes:
X^2 – ½X = 5/4
Step 3: T ake half the coefficient of X term and square it and add it to both sides
½ of -1/2 =-1/4
When you square it you have 1/16 add to both side of the equation which now becomes:
X^2 - 1/2X + 1/16 = 5/4 + 1/16
Step 4: Convert the left hand side to a squared form and simplify the R.H.S
(x-1/2)^2 = 21/16 (now you have a simple squared form just like our first example)
Step 5: Find the square root of both sides
x-1/2 = + or – sqrt(21/16)
solving for x finally leads to 2 answers either :
X=1/2- sqrt(21/16) or X= ½ + sqrt(21/16)


Congratulations you have successfully complete the steps for solving a quadratic equation using completing the square method.
Summary:
Move the number part to the right hand side of the equation
Divide through by the coefficient of the x squared term
Take one-half the coefficient of the x term ,square it and add it to both sides of the equation
Re-arrange your equation by putting the right hand side in squared form and simplifying the left hand side
Take the square root of both sides remembering the + or – sign on the right hand side
Finally solve for two possible values of X
Exercise:
Solve X^2 +6X-7=0 by completing the square method
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