Question

\\\sqrt3{x} + 9 = 4\\

Explanation:

🆕 New Concept Discovered: Solving Radical Equations
Undo the root to find the variable.

Step 1: Isolate the radical term

Subtract \(9\) from both sides of the equation to get the cube root term by itself.

$$ \sqrt[3]{x} + 9 = 4 $$

$$ \sqrt[3]{x} = 4 - 9 $$

$$ \sqrt[3]{x} = -5 $$

Step 2: Eliminate the cube root

To undo a cube root (\(\sqrt[3]{\phantom{x}}\)), raise both sides of the equation to the third power (cube both sides).

$$ (\sqrt[3]{x})^3 = (-5)^3 $$

$$ x = -125 $$

Step 3: Verify the solution

Substitute \(x = -125\) back into the original equation to check the answer.

$$ \sqrt[3]{-125} + 9 = -5 + 9 = 4 $$

The solution is correct.

Answer:

\(x = -125\)