Question

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}

Answer 1

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

1. Take the square root of both sides:

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

2. Calculate the square root of 196:

\[
\sqrt{196} = 14
\]

3. Set up the two possible equations:

\[
x - 18 = 14 \quad \text{or} \quad x - 18 = -14
\]

4. Solve each equation:

For \(x - 18 = 14\):

\[
x = 14 + 18 = 32
\]

For \(x - 18 = -14\):

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

5. Therefore, the solutions to the equation are:

\[
\{32, 4\}
\]

So, the correct response is:

\(\{32, 4\}\)