+0  
 
0
63
1
avatar

Solve: sqrt(9x^2-4x+4)=2(3x-2)+sqrt(x)

 May 29, 2023
 #1
avatar
0

First, we need to isolate the square root on the left-hand side of the equation. We can do this by squaring both sides of the equation. This gives us:

9x^2-4x+4=(2(3x-2)+sqrt(x))^2

Expanding the right-hand side of the equation gives us:

9x^2-4x+4=12x^2-12x+4

Subtracting 12x^2-12x+4 from both sides of the equation gives us:

-3x^2+8x-0=0

Factoring the left-hand side of the equation gives us:

-(x-2)(3x-0)=0

This gives us two possible solutions for x:

x=2 x=0

However, the value of x=0 is not a valid solution, because it would make the square root on the left-hand side of the original equation undefined. Therefore, the only valid solution is x=2.

 May 29, 2023

3 Online Users

avatar
avatar