How do we complete the Square

Question: How do we complete the Square

We use complete the square in order to solve our everyday quadratic equations, we use this technique in order to rearrange the quadratic into a square equals a number format , such as: (x – 4)² = 5 

Lets Do a Problem step by step:
1.Divide the whole equation by the coefficient that is in the front of the x^2  so that the new coefficient becomes 1. As shown in the equation below with the -4:

−4x2+56x+0−4

=

0−4

2. Diustribute the division "subtract" the zero:

x2−14x+0

=

0

                    +0  = +0   

3. 

x2−14x

= 0

4. Find the magic number or the number that will help the equation on the left become a perfect square.
this an be found by dividing b and 2 then squaring the answer like this, b/2---> answer^2 = c
ax^2+bx+c: As shown below. Add that magic number to both sides.
−14÷2=−7→(−7)2=49.
x^2-14x      =0
             +49=+49c
5. factor then express in square form.

x2−14x+49

=

49

(x−7)(x−7) = 49 0

(x−7)2

=

49

6.Take the square root of both sides. remember the plus or minus sign. Take the square root of the perfect square.

(x−7)2−−−−−−√

=

±49−−√

x−7

=

±7

x−7 = ±7 +7 = +7

7. get x alone.

x

=

7±7

8. seperate and combine.

x2=7−7

=

0

x1=7+7

=

14

FINISHED

NOW TRY IT YOURSELF!!!

solve: x^2-4x+53

http://www.deltamath.com/student.html#a
http://www.purplemath.com/modules/sqrquad.htm