Question

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

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

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

{21,5}
left brace 21 comma 5 right brace

{214,−178}

Answer 1

To solve the quadratic equation \((x - 18)^2 = 196\) using square roots, we first take the square root of both sides:

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

Calculating the square root of 196 gives us:

\[
\sqrt{196} = 14
\]

So, we have two cases:

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

Now, we solve each case:

1. **Case 1**:
\[
x - 18 = 14
\]
Adding 18 to both sides:
\[
x = 14 + 18 = 32
\]

2. **Case 2**:
\[
x - 18 = -14
\]
Adding 18 to both sides:
\[
x = -14 + 18 = 4
\]

Thus, the solutions are:

\[
\{32, 4\}
\]

Therefore, the correct response is \(\{32, 4\}\).