Saturday, December 15, 2012

Factor the equation 21x^2 + 22x = 8.

First, we'll move all terms to one
side:


21x^2 + 22x - 8 =
0


We'll use the quadratic formula to factorize the
equation:


21x^2+22x-8=0


x1 =
[-b +/- sqrt(b^2 - 4ac)]/2a


We'll identify the coefficients
a,b,c:


a = 21


b =
22


c = -8


b^2 - 4ac = 484 +
672


sqrt (b^2 - 4ac) = sqrt
1156


sqrt (b^2 - 4ac) = 34


x1
= (-22+34)/2*21


x1 = 12/42


x1
= 6/21


x2 =  (-22-34)/2*21


x2
= -56/42


x2 = -28/21


We can
now factorize the quadratic:


21x^2+22x-8 = 21(x - x1)(x -
x2)


We'll substitute x1 and
x2


21x^2+22x-8 = 21(x - 6/21)(x +
28/21)


or


21x^2+22x-8
= (21x - 6)(21x + 28)

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