SOLUTION: square root sign 9x+67=x+5 (solve) Rewrite with a rational exponent small 6 square root sign 19. Convert to decimal notation 8.87*10^7. I had 8870000000. (I know this is incorrec

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Question 170220: square root sign 9x+67=x+5 (solve)
Rewrite with a rational exponent small 6 square root sign 19.
Convert to decimal notation 8.87*10^7. I had 8870000000. (I know this is incorrect)
Use rational exponents to write xy small 5*y small 1|6 (1&6 are small numbers)*2 small 1|3 (1&3 are small numbers)
I thank you in advance, for all your help.
I am a student and I am in need of help.

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
square root sign 9x+67=x+5 (solve)
sqrt(9x+67) = x+5
Square both sides to get:
9x+67 = x^2+10x+25
Rearrange:
x^2+x-42 = 0
Factor:
(x-7)(x+6) = 0
x = 7 or x = -6
=================================
Rewrite with a rational exponent small 6 square root sign 19.
Ans: 19^(1/6)
====================================
Convert to decimal notation 8.87*10^7. I had 8870000000. (I know this is incorrect)
Ans: 8.87*10^7= 887*10^5 = 88700000
------------------------------------------
Use rational exponents to write xy small 5*y small 1|6 (1&6 are small numbers)*2 small 1|3 (1&3 are small numbers)
Comment: That is too confusing for me.
=========================================
Cheers,
Stan H.

Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Stanbon's solution is
incorrect because he did
not check for extraneous
solutions:


 (solve)

Square both sides:





Get 0 on the left:

Switch sides:

Factor

Use the zero-factor principle:

 

Stanbon quit here, but you MUST check
radical equations for extraneous solutions:

Checking 







That checks.

Checking 







This does not check so we
must discard  as
an extraneous solution. The
only solution is .

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

Rewrite with a rational exponent .

Use the rule 

.


Convert to decimal notation . I had . (I know this is incorrect)

Yes, you don't put on 7 zeros. You put on just enough
zeros so that you can move the decimal 7 places right.
You are to move the decimal of  7 places right.
There are only 2 decimal places showing so you will
need to put on 5 zeros so there will be 7 places. So you
consides  as  and then when you
move the decimal 7 places to the right, it will go at the
end and be invisible:

So  

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

Use rational exponents to write xy small 5*y small 1|6 (1&6 are small numbers)*2 small 1|3 (1&3 are small numbers)

I think you meant this:



Write the  as 



Write  as 
Write  as 




Then multiply under the radicals:



Edwin

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