Help me solve this radical equation.

Question

I realize that I didn't properly type out my problem last time. If someone could help me solve this problem, that would be great. Thank you!

x-6=√(19x+36)

Answer 1

Square both sides of the equation. 

 

X^{2 -} 12x +36=19x+36. Simplifying

x² -31x=0. Factor

x(X-31)=0. 

X=0,31. Both check so none are extraneous. 

 

Answer 2

x-6=√(19x+36)

 

Square both sides:

(x - 6)² = 19x + 36

x² - 12x + 36 = 19x + 36

x² - 31x = 0

x(x - 31) = 0

 

Then x = 0 or x - 31

 

Since both sides of the equation was squared, each value has to be checked because one of them may be extraneous, not a real solution.  This is because the square root would only give a positive value.

 

For x = 0, 0 - 6 = -6 ≠ √(0 +36) = √(36) = 6 => 0 is not a solution.

 

For x = 31, 31 - 6 = 25 = √(589 + 36) = √(625) = 25 => 31 is a solution.

 

From this the only solution is x = 31