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

2 Answers

Answer:

#x_1=2/3#
#x_2=-1/2#

Explanation:

From the given equation #6x^2-2=x#

Transpose the x term to the left of the equation

#6x^2-2=x#

#6x^2-x-2=0#

We can solve this by factoring method

#(3x - 2)(2x + 1 )=0#

After factoring, equate each factor to 0
First factor equate to 0
#3x-2=0#

#3x=2#

#(3x)/3=2/3#

#(cancel3x)/cancel3=2/3#

#x=2/3#

Second factor equate to 0
#2x+1=0#
#2x=-1#

#(2x)/2=(-1)/2#

#(cancel2x)/cancel2=(-1)/2#

#x=-1/2#

God bless....I hope the explanation is useful.

Mar 29, 2016

Answer:

#x=2/3,-1/2#

Explanation:

#color(blue)(6x^2-2=x#

Subtract #x# both sides

#rarr6x^2-2-x=cancel(x-x#

#rarr6x^2-2-x=0#

Rewrite in standard form

#rarrcolor(purple)(6x^2-x-2=0#

Now,this is a Quadratic equation (in form #ax^2+bx+c=0#)

Use Quadratic formula

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

Remember that #a,# #bandc# are the coeficients of #x^2,# #xand -2#

Where

#color(red)(a=6,b=-1,c=-2#

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

#rarrx=(1+-sqrt(1-4(6)(-2)))/(12)#

#rarrx=(1+-sqrt(1-(-48)))/(12)#

#rarrx=(1+-sqrt(1+48))/(12)#

#rarrx=(1+-sqrt(49))/(12)#

#color(orange)(rarrx=(1+-7)/(12)#

Now we have #2# solutions

#color(violet)(x=(1+7)/(12)=8/12=2/3#

#color(indigo)(x=(1-7)/(12)=-6/12=-1/2#

#color(blue)( :.ul bar |x=2/3,-1/2|#