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

Question

Responses

​ {−4,−32}

{21,5}

{214,−178}

{32,4}

Answer 1

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

1. Take the square root of both sides: \[ x - 18 = \pm 14 \]

2. Solve for \(x\) for both cases:

   Case 1: \[ x - 18 = 14 \] \[ x = 14 + 18 = 32 \]

   Case 2: \[ x - 18 = -14 \] \[ x = -14 + 18 = 4 \]

So, the solutions are \(x = 32\) and \(x = 4\).

Thus, the correct response is: {32, 4}.