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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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      Log On


   

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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
Stanbon's solution is
incorrect because he did
not check for extraneous
solutions:

sqrt%289x%2B67%29=x%2B5 (solve)

Square both sides:

%28sqrt%289x%2B67%29%29%5E2=%28x%2B5%29%5E2

9x%2B67=%28x%2B5%29%28x%2B5%29
9x%2B67=x%5E2%2B10x%2B25
Get 0 on the left:
0=x%5E2%2Bx-42
Switch sides:
x%5E2%2Bx-42=0
Factor
%28x-6%29%28x%2B7%29=0
Use the zero-factor principle:

 

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

Checking x=6

sqrt%289x%2B67%29=x%2B5
sqrt%289%286%29%2B67%29=%286%29%2B5
sqrt%2854%2B67%29=6%2B5
sqrt%28121%29=11
11=11

That checks.

Checking x=-7

sqrt%289x%2B67%29=x%2B5
sqrt%289%28-7%29%2B67%29=%28-7%29%2B5
sqrt%28-63%2B67%29=-7%2B5
sqrt%284%29=-2
2=-2

This does not check so we
must discard x=-7 as
an extraneous solution. The
only solution is x=6.

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

Rewrite with a rational exponent root%286%2C19%29.

Use the rule root%28N%2CX%5EM%29=X%5E%28M%2FN%29

root%286%2C19%29=6%5E%281%2F19%29.

Convert to decimal notation matrix%281%2C3%2C8.87%2C%22%D7%22%2C10%5E7%29. I had 8870000000. (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 8.87 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 8.87 as 8.8700000 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:

xy%5E5%2Ay%5E%281%2F6%29%2A2%5E%281%2F3%29

Write the 1%2F3 as 2%2F6

xy%5E5%2Ay%5E%281%2F6%29%2A2%5E%282%2F6%29

Write y%5E%281%2F6%29 as root%286%2Cy%29
Write 2%5E%282%2F6%29 as root%286%2C2%5E2%29

xy%5E5%2Aroot%286%2Cy%29%2Aroot%286%2C2%5E2%29
xy%5E5%2Aroot%286%2Cy%29%2Aroot%286%2C4%29

Then multiply under the radicals:

xy%5E5%2Aroot%286%2C4y%29

Edwin