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: \[ x - 18 = \pm \sqrt{196} \] \(\sqrt{196} = 14\), so we have: \[ x - 18 = 14 \quad \text{and} \quad x - 18 = -14 \]

2. Solve for \(x\) in both cases:

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

3. Thus, the solutions are: \[ {32, 4} \]

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