Question

what is the first step to take to solve the radical equation $12 + \sqrt{x^4 - 10} = 8$?

• raise both sides of the equation to the second power.
• subtract 12 from both sides of the equation.
• add 10 to both sides of the equation.
• add 12 to both sides of the equation.

Explanation:

To solve a radical equation like \(12 + \sqrt{x^4 - 10} = 8\), the first step is to isolate the radical term. The radical here is \(\sqrt{x^4 - 10}\), and it is added to 12. To isolate the radical, we need to get rid of the 12 on the left side. Subtracting 12 from both sides will do that: \(12 - 12+ \sqrt{x^4 - 10} = 8 - 12\), which simplifies to \(\sqrt{x^4 - 10}=-4\). Raising both sides to a power should come after isolating the radical, and adding 10 or 12 would not isolate the radical. So the correct first step is to subtract 12 from both sides.

Answer:

Subtract 12 from both sides of the equation. (Corresponding option: Subtract 12 from both sides of the equation.)