How do you solve #3x^2+5x=2# by completing the square?

1 Answer
Oct 6, 2016

Answer:

#3(x+5/6)^2-49/12=y#

Explanation:

The goal of completing the square is to convert the equation into a perfect square trinomial. The benefit of this form is to be able to identify the vertex of a parabola very easily.

Factor out a 3

#3(x^2+5/3x)=2#

Take the coefficient from the x term and divide it by 2 and then square it.

#((5/3)/2)^2=(5/3*1/2)^2=(5/6)^2=25/36#

Include #25/36# on the left and include #3(25/36)# on the right because we factored out a 3 on the left in an earlier step.

#3(x^2+5/3x+25/36)=2+3(25/36)#

We now have a perfect square trinomial that can be written in a more compact form

#3(x+5/6)^2=2+3(25/36)#

Simplify

#3(x+5/6)^2=2+cancel3(25/(cancel36 12))#

#3(x+5/6)^2=2+(25/(12))#

Convert #2# to #24/12# so that we have common denominator.

#3(x+5/6)^2=24/12+(25/(12))#

#3(x+5/6)^2=49/12#

Subtract #49/12#

#3(x+5/6)^2-49/12=0#

#3(x+5/6)^2-49/12=y#

For more information please see the video tutorials below.