Completing the Square

Correct me if I'm wrong but we complete the square when factoring is not possible. Yes? If not, what is the main we must complete the square at times? Cam you illustrate with a simple example?

 

no

Completing the Square is a technique which can be used to find maximum or minimum values
of quadratic functions. We can also use this technique to change or simplify the form of algebraic
expressions.
What is meant by a complete or exact square ?
An expression of the form (x + a)^2 is called a complete or exact square. Recall that
(x + a)^2 = x^2 + 2ax + a^2

"Completing the Square" is where we take a Quadratic Equation like this:

ax^2 + bx + c = 0

and turn it into this:

a(x+d)^2 + e = 0

So, I can tell you that:
d = b/(2a)

and:
e = c - b^2/(4a)

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



As you can see x^2 + bx can be rearranged nearly into a square and we can complete the square with (b/2)^2.

 

You said:

"with a little inspiration from Geometry we can convert it, like this:" but your picture did not upload.
Convert it like what?

What is the relationship between completing the square and the quadratic formula?

 

from compete square you derive quadratic formula

 

Very nicely done.

See link below.

A Point Has No Measure