Solve for x

Problem

√(,6*x−2)=√(,4*x+4)

Solution

1. Square both sides of the equation to eliminate the radical signs.

(√(,6*x−2))2=(√(,4*x+4))2

6*x−2=4*x+4

2. Isolate the variable by subtracting 4*x from both sides of the equation.

2*x−2=4

3. Move the constant by adding 2 to both sides.

2*x=6

4. Solve for x by dividing both sides by 2

x=3

5. Verify the solution by substituting x=3 back into the original equation to ensure the radicands are non-negative and equal.

√(,6*(3)−2)=√(,18−2)=√(,16)=4

√(,4*(3)+4)=√(,12+4)=√(,16)=4

Final Answer

√(,6*x−2)=√(,4*x+4)⇒x=3

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