How do you solve \sqrt { 54+ 3x } = x?

3 Answers
Mar 29, 2017

x=9 or x=-6

Explanation:

Square both sides

54+3x=x^2

Take 54 and 3x from both sides

x^2-3x-54=0

Then we Differentiate

(x-9)(x+6)=0

x=9 or x=-6

Mar 29, 2017

x_1=9; x_2=-6

Explanation:

Squaring both sides, we can get the left side of the equation out of the square root.
54+3x=x^2
x^2-3x-54=0
(x-9)(x+6)=0

Hence, the roots of x are:
x_1=9 and x_2=-6

Mar 29, 2017

color(red)(x=9 and x=-6

Explanation:

sqrt(54+3x)=x

:.(sqrt(54+3x))^2=x^2

:.sqrt(54+3x)*sqrt(54+3x)=x^2

Note:

color(red)(sqrta*sqrta=a

:.x^2=54+3x

:.x^2-3x-54=0

:.(x-9)(x+6)=0

:.color(red)(x=9 and x=-6