Answer:
{12}
Step-by-step explanation:
isolate the radical expression
[tex]\sqrt{3x} = x-6[/tex]
raise both sides to the index of the radical in this case 2
[tex](\sqrt{3x} )^{2} = (x-6)^2[/tex]
[tex]3x = (x-6)^2[/tex]
foil the right hand side or multiply (x-6)(x-6)
[tex]3x = x^{2} -6x-6x+36[/tex]
subtract 3x from both sides and combine like terms
[tex]0=x^{2} -15x+36[/tex]
factor
[tex]0=(x-12)(x-3)[/tex]
set each factor equal to zero and solve for x
x - 12 = 0 and x - 3 = 0
x = 12 and x = 3
Check each answer by plugging them individually into the original equation if the come out true they are a solution.
Check :
[tex]\sqrt{3(12)}+10=12+4\\\sqrt{36}+10 = 8\\6+10 = 16\\16=16[/tex] [tex]\sqrt{3(3)}+10=3+4\\\sqrt{9}+10=7\\3+10=7\\13\neq 7[/tex]
So the only solution is 12.
