# Math Help - equations with radicals

here is the problem : 4 - √2-x = √x+6

square each side

(4-√2-x)^2 = (√x+6)^2

foil and simplfy

18-8√2-x bbbb -x = x + 6

pretty much stuck at this point tried adding x and subtracting 18 from left side and put on right but it just turned into a diaster

thanks!

2. Originally Posted by purified
here is the problem : 4 - √2-x = √x+6

square each side

(4-√2-x)^2 = (√x+6)^2

foil and simplfy

18-8√2-x bbbb -x = x + 6

pretty much stuck at this point tried adding x and subtracting 18 from left side and put on right but it just turned into a diaster

thanks!
Am I correct that this is $4- \sqrtt{2-x}= \sqrt{x+ 6}$?
Then squaring gives $16- 8\sqrt{2- x}+ 2- x= x+ 6$ which reduces to $18- 8\sqrt{2-x}- x= x+ 6$, just as you say. Now get the square root by itself, $-8\sqrt{2-x}= 2x- 12$, and square both sides, $64(2- x)= 4x^2- 48x+ 144$. Solve that quadratic equation for x.