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

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

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

{214,−178}

Answer 1

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

1. Take the square root of both sides:

   \[ x - 18 = \pm \sqrt{196} \]

2. Calculate the square root of 196:

   \(\sqrt{196} = 14\)

3. Set up the two equations:

   \[ x - 18 = 14 \quad \text{or} \quad x - 18 = -14 \]

4. Solve each equation:

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

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

5. List the solutions: The solutions to the equation are \(x = 32\) and \(x = 4\).

Thus, the solution set is \({32, 4}\).

The correct response is:

\({32, 4}\) left brace 32 comma 4 right brace.