Solve the following quadratic equation using square roots: (x−18)^2=196

To solve the quadratic equation \((x−18)^2 = 196\) using square roots, we can follow these steps:

1. Take the square root of both sides: \[ x - 18 = \pm \sqrt{196} \]

2. Calculate \(\sqrt{196}\): \[ \sqrt{196} = 14 \]

3. This gives us two equations: \[ x - 18 = 14 \quad \text{and} \quad x - 18 = -14 \]

4. Solve for \(x\) in each case:

   • For \(x - 18 = 14\): \[ x = 14 + 18 = 32 \]
   • For \(x - 18 = -14\): \[ x = -14 + 18 = 4 \]

5. Thus, the solutions are: \[ x = 32 \quad \text{and} \quad x = 4 \]

So, the solutions to the original equation are \({32, 4}\).

The correct response from your options is: {32, 4}.