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

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

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

{214,−178}

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: \[ x - 18 = \pm 14 \] (since \( \sqrt{196} = 14\))

2. Now, solve for \(x\) in both cases:

   a. For the positive case: \[ x - 18 = 14 \] \[ x = 14 + 18 = 32 \]

   b. For the negative case: \[ x - 18 = -14 \] \[ x = -14 + 18 = 4 \]

Thus, the solutions for the equation \((x - 18)^2 = 196\) are: \[ {32, 4} \]

So, the correct response is: \({32, 4}\) (left brace 32 comma 4 right brace).