the squared root of 3x equals x-6, what is the value of x

Question

This question is about the squared root of a number and and variable equaling a variable subtracted by a number.  I need to solve for X.

Answer 1

√(3x) = x - 6

 

 

Square both sides of the equation to undo the radical.

 

3x = (x - 6)²

 

3x = x² - 12x + 36

 

 

Subtract 3x on both sides of the equation.

 

0 = x² - 15x + 36

 

 

Factor using FOIL.

 

0 = (x - 12)(x - 3)

 

x = 12          and           x = 3

 

 

Reject  x=3  because

 

√(3(3)) = 3 - 6

 

√9 = -3

 

3 = -3

 

Not true.

 

 

x=12 is the only solution.