Question

How do I solve this equation and check the solutions?

Answer 1

Answer:

{12}

Step-by-step explanation:

isolate the radical expression

$\sqrt{3x} = x-6$

raise both sides to the index of the radical in this case 2

$(\sqrt{3x} )^{2} = (x-6)^2$

$3x = (x-6)^2$

foil the right hand side or multiply (x-6)(x-6)

$3x = x^{2} -6x-6x+36$

subtract 3x from both sides and combine like terms

$0=x^{2} -15x+36$

factor

$0=(x-12)(x-3)$

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 :

$\sqrt{3(12)}+10=12+4\\\sqrt{36}+10 = 8\\6+10 = 16\\16=16$           $\sqrt{3(3)}+10=3+4\\\sqrt{9}+10=7\\3+10=7\\13\neq 7$

So the only solution is 12.

Answer 2

Answer:

10+√3=4x²

Step-by-step explanation: