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avatar+255 

Solve x - 6 = sqrt(3x).

 Feb 17, 2021
 #1
avatar+294 
+2

Let's solve your equation step-by-step.

x−6=√3x

Step 1: Flip the equation.

√3x=x−6

Step 2: Solve Square Root.

√3x=x−6

3x=(x−6)2(Square both sides)

3x=x2−12x+36

3x−(x2−12x+36)=x2−12x+36−(x2−12x+36)(Subtract x^2-12x+36 from both sides)

−x2+15x−36=0

(−x+3)(x−12)=0(Factor left side of equation)

−x+3=0 or x−12=0(Set factors equal to 0)

x=3 or x=12

Check answers. (Plug them in to make sure they work.)

x=3(Doesn't work in original equation)

x=12(Works in original equation)

 Feb 17, 2021
 #2
avatar+32894 
+2

Square both sides to get

x^2 -12x+36  = 3x   simplify

(x^2 - 15x + 36) = 0                   factor

(x-12)(x-3) = 0      so x = 12 or 3      

 

sub into original equation to find if they work    12 does      3 is extraneous

 Feb 17, 2021

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