Question

Solve the following quadratic equation using square roots: (x−18)^2=196.(1 point)
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 equation \((x - 18)^2 = 196\) using square roots, we start by taking the square root of both sides:

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

Calculating the square root of 196 gives:

\[
\sqrt{196} = 14
\]

Thus, we have two cases to consider:

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

Now, solve each case:

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

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

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

\[
\{32, 4\}
\]

So, the correct response is:

\(\{32, 4\}\) (left brace 32 comma 4 right brace)