Solve the following quadratic equation using square roots: (x−18)2=196.(1 point)

Question

Responses

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

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

{32,4}
left brace 32 comma 4 right brace

{21,5}

Answer 1

To solve the 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 the square root of 196: \[ \sqrt{196} = 14 \] Therefore, the equation becomes: \[ x - 18 = \pm 14 \]

3. This gives us two cases to solve for \(x\):

   • Case 1: \(x - 18 = 14\) \[ x = 14 + 18 = 32 \]

   • Case 2: \(x - 18 = -14\) \[ x = -14 + 18 = 4 \]

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

Therefore, the correct response is: \({32, 4}\)