Question

\\\sqrt3{x} + 7 = 2\\

Explanation:

🆕 New Concept Discovered: Solving Radical Equations
Undo roots by raising both sides to the matching power.

Step 1: Isolate the radical term

To solve for \(x\), we first need to get the cube root term by itself on one side of the equation. We do this by subtracting \(7\) from both sides:

$$ \sqrt[3]{x} + 7 - 7 = 2 - 7 $$

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

Step 2: Eliminate the cube root

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

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

$$ x = (-5) \times (-5) \times (-5) $$

$$ x = -125 $$

Step 3: Verify the solution

We substitute \(x = -125\) back into the original equation to make sure it works:

$$ \sqrt[3]{-125} + 7 = -5 + 7 = 2 $$

Since \(2 = 2\), the solution is correct.

Answer:

$$ x = -125 $$