Solve the 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. Remember to consider both the positive and negative square roots:

   \[ x - 18 = \pm \sqrt{196} \]

2. Calculate the square root of 196:

   \[ \sqrt{196} = 14 \]

   So the equation becomes:

   \[ x - 18 = \pm 14 \]

3. Now, split this into two separate equations:

   • First equation: \[ x - 18 = 14 \]

     Adding 18 to both sides gives:

     \[ x = 14 + 18 = 32 \]

   • Second equation: \[ x - 18 = -14 \]

     Adding 18 to both sides gives:

     \[ x = -14 + 18 = 4 \]

4. Therefore, the solutions to the equation \((x - 18)^2 = 196\) are:

   \[ x = 32 \quad \text{and} \quad x = 4 \]

So, \(x = 32\) and \(x = 4\) are the final answers.