How do you solve #6x^2 - x -3 =0#?

1 Answer
Nov 22, 2015

Answer:

#x~~ -0.63 , color(white)(xx) x~~0.79#

Explanation:

It is a matter of practice so that you get used to spotting the factors.

The only 2 factors you are going to get for 3 is 1 and 3. This is because 3 is a prime number. The thing is that we have -3 so one has to be positive and the other negative.
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Factors of 3 are only {1,3} because 3 is a prime number

Factors of 6 are {1,6} , {2,3}

Looking for -1 in #-x#

These factors do not work so revert to the standard solution formula:

#ax^2+bx+c=0#

where
#x=(-b+-sqrt(b^2-4ac))/(2a)#

#a=6#
#b=-1#
#c=-3#

#x=(-(-1)+-sqrt((-1)^2-4(6)(-3)))/(2(6))#

#color(green)("The use of brackets round negative numbers reduce")#
#color(green)("the chance of making a mistake!")#

#x=(1+-sqrt(1+72))/12#

#x=1/12 +- sqrt(73)/12#

#x~~0.08dot3 +-0.71#

#x~~ -0.63 , x~~0.79#