How do you solve the equation #6x^2-5x-13=x^2-11# by completing the square?

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Answer 1 · 2017-08-20T02:50:33

#x=sqrt(13/20)+1/2#
#x=-sqrt(13/20)+1/2#

Given -

#6x^2-5x-13=x^2-11#

Take all the terms to the left-hand side

#6x^2-5x-13-x^2+11=0#

Simplify it.

#5x^2-5x-2=0#

Take the constant term to the right-hand side

#5x^2-5x=2#

Divide all the terms by the coefficient of #x^2#

#(5x^2)/5-(5x)/5=2/5#

#x^2-x=2/5#

Take half the coefficient of #x#, square it and add it to both sides

#x^2-x+1/4=2/5+1/4=(8+5)/20=13/20#

#(x-1/2)^2=13/20#

#(x-1/2)=+-sqrt(13/20)#

#x=sqrt(13/20)+1/2#
#x=-sqrt(13/20)+1/2#