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

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This Lesson (Completeing the Square and Quadratic Equation (how to find and use it)) was created by by Nate(3495) About Me : View Source, Show
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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 x squared
(x + 1)^2 = 1 - 1 sum 1^2 with the other term on the other side of the equation
(x + 1)^2 = 0
x + 1 = 0
x = -1
graph(300,300,-5,5,-5,5,x^2+2x+1,0)
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
graph(300,300,-5,5,-5,5,2x^2+6x+4,0)
Now, the quadratic formula:
ax^2 + bx + c = 0
ax^2 + bx = -c
x^2 + bx/a = -c/a
(x + b/(2a))^2 = b^2/(4a^2) - c/a = b^2/(4a) - 4ac/(4a^2) = (b^2 - 4ac)/(4a^2)
x + b/2a = +- sqrt(b^2 - 4ac)/(2a)
x = (-b +- sqrt(b^2 - 4ac))/(2a)
How to use it:
Ex.) 3x^2 + 7x + 2 = 0
Remember: ax^2 + bx + c = 0
a=3 and b=7 and c=2
x = (-b +- sqrt(b^2 - 4ac))/(2a)
x = (-7 +- sqrt(7^2 - 4*3*2))/(6)
x = (-7 +- sqrt(49 - 24))/(6)
x = (-7 +- sqrt(25))/(6)
x = (-7 +- 5)/(6)
x = -2 and x = -1/3
graph(300,300,-5,5,-5,5,3x^2+7x+2,0)
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