Question

How do you solve `sqrt(6x-3) - 1 = x`?

Answer 1

`x=2`

Explanation:

`"isolate "sqrt(6x-3)" by adding 1 to both sides"`

`sqrt(6x-3)=x+1`

`color(blue)"square both sides"`

`(sqrt(6x-3))^2=(x+1)^2`

`6x-3=x^2+2x+1`

`"rearrange into "color(blue)"standard form ";ax^2+bx+c=0`

`"subtract "6x-3" from both sides"`

`0=x^2-4x+4`

`0=(x-2)^2rArrx=2`

`color(blue)"As a check"`

Substitute this value into the equation and if both sides are equal then it is the solution.

`"left "=sqrt(12-3)-1=sqrt9-1=3-1=2=" right"`

`x=2" is the solution"`