Question

\\10 = 5\sqrt{x - 4}\\

Explanation:

🆕 New Concept Discovered: Solving Radical Equations
Isolate the radical, square both sides, and solve.

Step 1: Isolate the radical term

To get the radical term by itself, divide both sides of the equation by \(5\):

$$ \frac{10}{5} = \frac{5\sqrt{x - 4}}{5} $$

$$ 2 = \sqrt{x - 4} $$

Step 2: Eliminate the radical

To undo the square root, square both sides of the equation:

$$ (2)^2 = (\sqrt{x - 4})^2 $$

$$ 4 = x - 4 $$

Step 3: Solve for x

Add \(4\) to both sides to isolate \(x\):

$$ 4 + 4 = x $$

$$ x = 8 $$

Step 4: Verify the solution

Substitute \(x = 8\) back into the original equation to check for extraneous solutions:

$$ 10 = 5\sqrt{8 - 4} $$

$$ 10 = 5\sqrt{4} $$

$$ 10 = 5(2) $$

$$ 10 = 10 \quad \text{(True)} $$

Answer:

\(x = 8\)