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How do you solve #3x^2-4x-2=0# by completing the square?

Answer 1

James Allen

#x=2/3+sqrt(10)/3# , #x=2/3-sqrt(10)/3#

Firstly, we need to deal with the coefficient of #x^2# (the 3).

We divide the entire expression by 3 to get rid of the 3.

#(3x^2-4x-2)/3=0/3#

#x^2-4/3x-2/3=0#

After finishing the square, the general formula is as follows.

#x^2+ax=(x+a/2)^2-(a/2)^2#

thus applying this formula,

#x^2-4/3x-2/3=0#

goes to

#(x-4/6)^2-16/36-2/3=0#

Reducing in complexity,

#(x-2/3)^2-10/9=0#

reorganize to accommodate x,

#(x-2/3)^2= 10/9#

#x-2/3= +-sqrt(10/9)#

#x=2/3+sqrt(10)/3# , #x=2/3-sqrt(10)/3#

These two are the answers.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.