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

Question

Responses

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

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

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

​ {−4,−32}

Answer 1

To solve the equation \((x - 18)^2 = 196\) using square roots, follow these steps:

1. Take the square root of both sides: \[ x - 18 = \pm \sqrt{196} \]

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

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

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

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

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

Thus, the solutions to the equation \((x - 18)^2 = 196\) are \(x = 32\) and \(x = 4\).

The final solution set is \({ 32, 4 }\).

So the correct response is: \[ {32, 4} \]