Lesson Completeing the Square and Quadratic Equation (how to find and use it)

Firstly, let us discover: Completeing the Square
Ex.) x^2 + 2x + 1 = 0
x^2 + 2x = -1 leave all the x-terms on one side
(x + 1)^2 = -1 sum half of the linear term to squared
(x + 1)^2 = 1 - 1 sum with the other term on the other side of the equation
(x + 1)^2 = 0
x + 1 = 0
x = -1

Lets try a harder one now:
Ex.) 2x^2 + 6x + 4 = 0
2x^2 + 6x = -4
x^2 + 3x = -2 divide everything by two to get your leading coefficient to be positive one
(x + 3/2)^2 = 9/4 - 2 = 9/4 - 8/4 = 1/4
x + 3/2 = +- 1/2
x = -3/2 +- 1/2
x = -2 and x = -1

Now, the quadratic formula:




= +-

How to use it:
Ex.) 3x^2 + 7x + 2 = 0
Remember: ax^2 + bx + c = 0
a=3 and b=7 and c=2





and