Solve for x square root of 3x+x=0

Problem

√(,3*x)+x=0

Solution

1. Isolate the radical term by subtracting x from both sides of the equation.

√(,3*x)=−x

2. Square both sides of the equation to eliminate the square root.

(√(,3*x))2=(−x)2

3*x=x2

3. Rearrange the equation into a standard quadratic form by subtracting 3*x from both sides.

x2−3*x=0

4. Factor the quadratic expression by taking out the greatest common factor, which is x

x*(x−3)=0

5. Solve for x by setting each factor equal to zero.

x=0

x−3=0⇒x=3

6. Check for extraneous solutions by substituting the values back into the original equation. For x=0 √(,3*(0))+0=0 which is true. For x=3 √(,3*(3))+3=3+3=6≠0 Therefore, x=3 is extraneous.

Final Answer

√(,3*x)+x=0⇒x=0

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