Question

Solve the equation √x - 6 + 2 = 6 for the variable. Show each step of your solution process.

Answer 1

To solve the equation \(\sqrt{x} - 6 + 2 = 6\), you combine like terms and isolate the root, then solve by squaring both sides, yielding \(x = 100\). Upon checking, the solution is verified to be correct.

Step-by-step explanation:

To solve the equation \(\sqrt{x} - 6 + 2 = 6\), we must isolate the variable x. We begin by combining like terms and isolating the square root:

1. Add 6 to both sides of the equation: \(\sqrt{x} - 6 + 6 + 2 = 6 + 6\).
2. Simplify both sides: \(\sqrt{x} + 2 = 12\).
3. Subtract 2 from both sides: \(\sqrt{x} = 10\).
4. To remove the square root, square both sides of the equation: \((\sqrt{x})^2 = 10^2\).
5. Simplify to find the value of x: \(x = 100\).

Thus, the solution to the equation is \(x = 100\). Lastly, we check if our solution makes sense by substituting the value back into the original equation:

1. Substitute 100 for x: \(\sqrt{100} - 6 + 2\).
2. Since \(\sqrt{100} = 10\), the equation becomes: \(10 - 6 + 2\).
3. Which simplifies to: \(10 - 4 = 6\).
4. And \(6 = 6\), which confirms our solution is correct.