Solve the following quadratic equation using square roots: (x - 18)? = 196. (1 point)

Question

0 (32,4}
0 {21,5}
• 1-4, -32}
• 1214, - 178}

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 of the equation: \[ x - 18 = \pm \sqrt{196} \]

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

3. Now, set up two equations: \[ x - 18 = 14 \quad \text{or} \quad x - 18 = -14 \]

4. Solve each equation for \(x\):

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

5. The solutions are \(x = 32\) and \(x = 4\).

The solution set is: \[ {32, 4} \]

From the options provided, the correct answer is: \[ {32, 4} \]