Solve for x

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• Aug 3rd 2010, 05:00 AM
saha.subham
Solve for x
21x^2 - 83x + 34 = 0

i know i will get two values of ex by factorization. but i am not being able to middle term factorize it.
• Aug 3rd 2010, 05:22 AM
Wilmer
Try the quadratic formula.
• Aug 3rd 2010, 05:27 AM
eumyang
Quote:

Originally Posted by saha.subham
21x^2 - 83x + 34 = 0

i know i will get two values of ex by factorization. but i am not being able to middle term factorize it.

It's not factorable. For it to be factorable over the integers the discriminant would need to be a perfect square.
\displaystyle \begin{aligned} b^2 - 4ac &= (-83)^2 - 4(21)34 \\ &= 6889 - 2856 \\ &= 4033 \end{aligned}
... and 4033 is not a perfect square.
• Aug 4th 2010, 02:03 AM
HallsofIvy
Relatively few quadratics can be factored with integer coefficients. "Complete the square" or use the quadratic formula instead.
• Aug 4th 2010, 08:38 AM
pencil09
use quadratic formula
if $\displaystyle ax^2+bx+c=0$
then $\displaystyle x=\frac{-b\pm \sqrt{(b^2-4ac)}}{2a}$

-- hope it'll help --(Wink)