How do you solve #3x^2 – 24x + 24 = 0# using completing the square?

1 Answer
Jul 3, 2015

Answer:

Logical first step: divide everything by #3#

Explanation:

#->x^2-8x+8=0#

Completing the square would mean: taking half of the #x#-coefficient and squaring that:
#x^2-8x+(-4)^2=x^2-8x+16=(x-4)^2#

But we still have to balance the #16# with the #8# we had:
#->x^2-8x+16-8=0#
#->(x-4)^2-8=0->(x-4)^2=8#

So #x-4=sqrt8=2sqrt2->x=4+2sqrt2#
Or #x-4=-sqrt8=-2sqrt2->x=4-2sqrt2#

Often written as #x_(1,2)=4+-2sqrt2#