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

1 answer

To solve the equation (x18)2=196 using square roots, follow these steps:

  1. Take the square root of both sides of the equation: x18=±196

  2. Calculate the square root of 196: 196=14 Therefore, the equation becomes: x18=±14

  3. This gives us two cases to solve for x:

    • Case 1: x18=14 x=14+18=32

    • Case 2: x18=14 x=14+18=4

  4. Thus, the solutions are: x=32andx=4

Therefore, the correct response is: 32,4