Answer:
x=5
Step-by-step explanation:
Given
[tex]x=\sqrt{3x+10}[/tex]
Squaring on both sides
[tex]x^2=(\sqrt{3x+10})^2 \\x^2=3x+10\\x^2-3x-10 = 0\\x^2-5x+2x-10 = 0\\x(x-5)+2(x-5) = 0\\(x-5)(x+2)=0\\x=5\\and\\x=-2[/tex]
Since putting -2 gives us:
[tex]-2=\sqrt{3(-2)+10} \\-2=\sqrt{-6+10}\\-2=\sqrt{4}\\-2\neq 2[/tex]
2 is an extraneous solution.
Therefore, the solution to x=√3x+10 is x=5 ..
