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

Question

.(1 point)
Responses

{21,5}
left brace 21 comma 5 right brace

​ {−4,−32}
​ left brace negative 4 comma negative 32 right brace

{214,−178}
left brace 214 comma negative 178 right brace

{32,4}

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. Therefore, we have two cases: \[ x - 18 = 14 \quad \text{or} \quad x - 18 = -14 \]

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

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

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

Thus, the final answer is: \[ {32, 4} \]

The correct response is \({32, 4}\).