Solve the following quadratic equation using square roots: (x−18)exponent2=196 .(1 point)

Question

Responses

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

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

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

{32,4}

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

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

   • For the first equation: \[ x - 18 = 14 \implies x = 14 + 18 = 32 \]
   • For the second equation: \[ x - 18 = -14 \implies x = -14 + 18 = 4 \]

5. Write the solution set: \[ {32, 4} \]

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