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Can you please help explain this problem in a simple way?

Square root of 7-3x +3 = x

 

Thank you!

 
 Jun 4, 2021
 #1
avatar+119772 
+1

I guess this  is supposed  to  be

 

sqrt ( 7 - 3x)  +  3  =  x                

 

sqrt ( 7 - 3x)   =  x - 3         (1)              square  both sides

 

7 - 3x  =   (x - 3)^2

 

7 - 3x   =  x^2  - 6x   +  9

 

x^2  -6x  + 9  - 7  + 3x   =  0

 

x^2  - 3x  +  2   =   0          factor

 

(x - 2)  ( x - 1)  =  0

 

Setting   each  factor  to  0 and solving for  x    gives us

 

x = 2      or    x   =  1

 

However, looking at (1)......either  value of  x produces  a negative  value  on  the right.....and  we  can  never get a negative  value   from the positive root on the left

 

So.....we  have no real solutions

 

 

cool cool cool

 
 Jun 4, 2021
 #2
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Thank you so much! 

I understand it!

 
 Jun 4, 2021
 #3
avatar+119772 
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OK.......glad to  help   !!!!

 

 

cool cool cool

 
CPhill  Jun 4, 2021

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