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

Answer 1

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

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

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

3. Set up the two equations: \[ x - 18 = 14 \quad \text{or} \quad x - 18 = -14 \]

4. Solve each equation:

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

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

5. Conclude the solutions: The solutions to the equation \((x-18)^2 = 196\) are: \[ x = 32 \quad \text{and} \quad x = 4 \]

Thus, the final answers are \(\boxed{32}\) and \(\boxed{4}\).