Find the Domain square root of 4x+40=2x-4

Problem

√(,4*x+40)=2*x−4

Solution

1. Identify the restriction for the square root function, which requires the radicand (the expression inside the square root) to be greater than or equal to zero.

Radicand≥0

2. Set up the inequality for the radicand of the square root on the left side of the equation.

4*x+40≥0

3. Solve the inequality by subtracting 40 from both sides.

4*x≥−40

4. Divide both sides by 4 to isolate x

x≥−10

5. Consider the range restriction of a principal square root, which must be non-negative. This implies the right side of the equation must also be greater than or equal to zero for a real solution to exist.

2*x−4≥0

6. Solve this second inequality by adding 4 to both sides and then dividing by 2.

2*x≥4

x≥2

7. Determine the intersection of the two conditions (x≥−10 and x≥2. The more restrictive condition defines the domain where the equation is defined and potentially solvable.

x≥2

Final Answer

Domain=[2,∞)

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