How do you solve #2x^2 - x = 6# graphically and algebraically?

1 Answer
A08
Mar 25, 2016

#x=2, and -3/2#
#-3/2 "can also be written as" -1.5#

Explanation:

Let's draw graph of the expression using graphing tool.
graph{2x^2-x-6 [-9.86, 10.14, -7.64, 2.36]}
Observe in the graph where it intersects #x# axis.
#(-1.5,0) and (2,0)#
#-1.5 and 2# are solutions of the equation.

Given equation is #2x^2-x=6#.
Taking all terms to left hand side we get
#2x^2-x-6=0#
Let's try split the middle term method.
Product of first and third term #=-12x^2#
Let's find two parts of middle term so that their product is equal to above. #12# has factors of #6 xx 2, 4 xx 3, 12 xx 1#. We see that #4xx3# parts work for us. Splitting middle term as in two parts #-4x and 3x# we obtain

#2x^2-4x+3x-6=0#, pair first two and last two
#(2x^2-4x)+(3x-6)=0#, Take out Common factor #2x# out of first pair and #3# out of second pair.
#2x(x-2)+3(x-2)=0#, Take out Common factor #x-2# out of two
#(x-2)(2x+3)=0#, Set each factor equal to #0#
#(x-2)=0# .......(1)
#(2x+3)=0# .....(2)
From (1) #x=2#
From (2) #x=-3/2#

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