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

2 Answers
Jun 6, 2018

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

Jun 6, 2018

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