<PRE><B>Question 1016061</B>
{{{(x-6)^2/2}}} +4 = 36
subtract 4 from both sides
{{{(x-6)^2/2}}} = 32
multiply both sides by 2
(x-6)^2 = 64
FOIL (x-6)(x-6)
x^2 - 6x - 6x + 36 = 64
combine like terms on the left
x^2 - 12x + 36 - 64 = 0
x^2 - 12x - 28 = 0
Factors to
(x-14)(x+2) = 0
two solutions
x = 14 
and
x = -2
:
Check both solutions in the original equation
x = 14
{{{(14-6)^2/2}}} +4 = 36
{{{8^2/2}}} +4 = 36
{{{64/2}}} +4 = 36
32 + 4 = 36; a good solution
and
x= -2
{{{(-2-6)^2/2}}} +4 = 36
{{{(-8)^2/2}}} +4 = 36
{{{64/2}}} +4 = 36
32 + 4 = 36; also OK
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