How do you solve #2x ^ { 2} - x - 15= 0#?

1 Answer
EZ as pi · War10ck
Nov 2, 2016

#x= -5/2 and x= +3#

Explanation:

You must find factors of the (#2x^2#) term and the (-15) term which give a (-x) term. In this situation it will be:

#" "2x^2 -x -15#

#" "2xcolor(white)(xxxxxx)5#
#" "1xcolor(white)(xxxxxx)3#

Cross multiply and subtract so:

#" "2xcolor(white)(xxxxx)+5" "rarr 1x xx +5 = +5x#
#" "1xcolor(white)(xxxxx)-3" "rarr 2x xx -3= -6x#

So you have: #" " 2x xx-3 = -6x and x xx5 = +5x#

The total is what you want:# -6x+5x = -x #

So your answer is: #(2x+5)(x-3) =0#

Setting each factor = 0 gives:

The roots are #-5/2 and +3#

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