Amira is solving the equation #x^2-6x = 1#. Which value must be added to both sides of the equation to make the left side a perfect square trinomial?

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Answer 1 · 2016-01-13T01:08:57

The value to add on both sides is #9#

The perfect square trinomial is

#(a+-b)^2=a^2+-2ab+b^2#

#x^2-6x=1#

#x^2-2*3x=1#

then

#2ab=2*3*x=2*x*3#

#a=x#
#b=3#

then we must add

#b^2=3^2=9#

#x^2-6xcolor(green)(+9)=1color(green)(+9)#

#x^2-6x+9=10#