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

Question

Responses

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

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

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

{21,5}

Answer 1

To solve the quadratic equation \((x - 18)^2 = 196\), we start by taking the square root of both sides:

\[ x - 18 = \pm \sqrt{196} \]

Calculating the square root:

\[ \sqrt{196} = 14 \]

Now we have two equations to solve:

1. \(x - 18 = 14\)
2. \(x - 18 = -14\)

Solving the first equation:

\[ x - 18 = 14 \implies x = 14 + 18 = 32 \]

Solving the second equation:

\[ x - 18 = -14 \implies x = -14 + 18 = 4 \]

Thus, the solutions to the equation \((x - 18)^2 = 196\) are:

\[ {32, 4} \]

So the correct response is:

\({32, 4}\)