SOLUTION: Solve the equations using the sq rt property {{{(3x-3)^2=81)}}} 3x-9= +/ sq rt 81 3x = 9 +/ sq rt 81 x = 9+/ sq rt 81/3 Should I reduce this all the way? It seems li

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Question 264754: Solve the equations using the sq rt property
%283x-3%29%5E2=81%29
3x-9= +/ sq rt 81
3x = 9 +/ sq rt 81
x = 9+/ sq rt 81/3
Should I reduce this all the way? It seems like a strange answer because 9,81,and 3 are all connected.

Found 4 solutions by jim_thompson5910, mananth, josmiceli, Edwin McCravy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%283x-3%29%5E2=81 Start with the given equation.


3x-3=%22%22%2B-sqrt%2881%29 Take the square root of both sides.


3x-3=sqrt%2881%29 or 3x-3=-sqrt%2881%29 Break up the "plus/minus" to form two equations.


3x-3=9 or 3x-3=-9 Take the square root of 81 to get 9.


3x=3%2B9 or 3x=3-9 Add 3 to both sides.


3x=12 or 3x=-6 Combine like terms.


x=4 or x=-2 Divide both sides by 3 to isolate x.


--------------------------------------


Answer:


So the solutions are x=4 or x=-2.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equations using the sq rt property
(3x-3)^2=81
(3x-3)^2=9^2
take sqrt of both
3x-3=9
3x=9+3
3x=12
x=4

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
%283x-3%29%5E2+=+81%29
You need to take the square root of both sides,
which you tried to do, but went astray.
If something is squared, then taking the
square root exactly cancels out the squaring.
In general:
sqrt%28n%5E2%29+=+n, so
sqrt%28%283x-3%29%5E2%29+=+sqrt%2881%29
3x+-+3+=+%2B9
and
3x+-+3+=+-9
From the 1st, I get
3x+=+12
x+=+4
From the 2nd, I get
3x+=+-6
x+=+-2
You can check these answers by plugging the number into
the original equation:
%283x-3%29%5E2+=+81%29
%283%2A4+-+3%29%5E2+=+81
9%5E2+=+81
81+=+81
and
%283x-3%29%5E2+=+81%29
%283%2A%28-2%29+-+3%29%5E2+=+81%29
%28-9%29%5E2+=+81
81+=+81
OK

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equations using the sq rt property
%283x-3%29%5E2=81%29

I'm afraid you made lots of mistakes.  Here is
how to solve it:

Take square roots of both sides, remembering ± on the
right side:

sqrt%28%283x-3%29%5E2%29=%22%22%2B-sqrt%2881%29%29

Take away both the 2 exponent and the square root on the left

3x-3=%22%22±sqrt%2881%29

When you get here you should immediately replace
sqrt%2881%29 by 9.

You should not keep the square root when you can take
the square root of what is under the radical.

Then you have

3x-3=%22%22±9

So yoiu make two equations, one using the +
and one using the -

3x-3=9 and 3x-3=-9

Solve the first equation and get x=4
Solve the second equation and get x=-2

Edwin