Question

What is the solution to x=√3x+10?

Answer 1

x=5

Explanation:

Given

`x=√(3x+10)`

Squaring on both sides

`x^2=(√(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`

Since putting -2 gives us:

`-2=√(3(-2)+10) \\-2=√(-6+10)\\-2=√(4)\\-2\\eq 2`

2 is an extraneous solution.

Therefore, the solution to x=√3x+10 is x=5 ..