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

2 Answers
Apr 24, 2017

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

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