Question

How do you solve `sqrt( 11x+3) -2x =0`?

Answer 1

`x=-1/4` and `x=3`

Explanation:

`sqrt( 11x+3) -2x =0`

Isolate the radical:

`sqrt( 11x+3)=2x`

`(sqrt( 11x+3))^2=(2x)^2`

`11x+3=4x^2`

`0=4x^2 -11x-3`

Factor:

`(4 x + 1) (x - 3) =0`

`x=-1/4` and `x=3`

Answer 2

`x = (13 + sqrt217)/8 or (13 - sqrt217)/8`

Explanation:

`sqrt(11x + 3) - 2x = 0`

Add `2x` to both sides;

`sqrt(11x + 3) - 2x + 2x = 0 + 2x`

`sqrt(11x+3) = 2x`

Square both sides;

`sqrt(11x + 3)^2 = (2x)^2`

`11x + 3 = 4x^2`

Rearranging the equation;

`4x^2 - 11x - 3 = 0`

Using the Quadratic Formula;

`x= (-b+-sqrt(b^2 - 4ac))/(2a)`

Where;

`a= 4`

`b= -11`

`c =-3`

Substituting the values into the equation..

`x = (-(-13) +- sqrt((-13)^2- 4(4)(-3)))/(2(4))`

`x= (13 +- sqrt(169 + 48))/8`

`x = (13 +- sqrt217)/8`

`x = (13 + sqrt217)/8 or (13 - sqrt217)/8`