How do you solve the equation #1/2(x-4)^2=8#?

2 Answers
Apr 24, 2017

Answer:

#color(blue)(x=8,0#

Explanation:

Solve:

#1/2(x-4)^2=8#

Multiply both sides by #2#.

#color(red)cancel(color(black)(2))xx1/color(red)cancel(color(black)(2))(x-4)^2=8xx2#

Simplify.

#(x-4)^2=16#

Take the square root of both sides.

#sqrt((x-4)^2)=+-sqrt16#

Simplify.

#x-4=+-4#

Add #4# to both sides and solve for #x#.

#x=4+-4#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#x=4-4#

#x=0#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#x=4+4#

#x=8#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#x=8,0#

Apr 24, 2017

Answer:

#x=0# and #x=8#
or
#x=0,8#

Explanation:

Order of operations.
Exponents first.
#1/2(x-4)^2=8# #---># #1/2(x^2-8x+16)=8#

Now divide both sides by #1/2#

#cancel(1/2)(x^2-8x+16)=8-:1/2#

#x^2-8x+16=16#

Subtract 16 from both sides

#x^2-8xcancel(+16)=cancel16#
#x^2-8x=0#

Factor "x"
#x(x-8)=0#

So now we have
#x=0# and #x-8=0#

Therefore,
#x=0# and #x=8#
or
#x=0,8#