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

Question

.(1 point)
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, we 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: \[ \sqrt{196} = 14 \]

3. This gives us two equations to solve: \[ x - 18 = 14 \quad \text{and} \quad x - 18 = -14 \]

4. Solve the first equation: \[ x - 18 = 14 \implies x = 14 + 18 \implies x = 32 \]

5. Solve the second equation: \[ x - 18 = -14 \implies x = -14 + 18 \implies x = 4 \]

Thus, the solutions to the equation are \(x = 32\) and \(x = 4\).

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