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

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

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

{32,4}

Answer 1

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

1. Take the square root of both sides:
\[
x - 18 = \pm \sqrt{196}
\]
\(\sqrt{196} = 14\), so we have:
\[
x - 18 = 14 \quad \text{and} \quad x - 18 = -14
\]

2. Solve for \(x\) in both cases:
- For \(x - 18 = 14\):
\[
x = 14 + 18 = 32
\]
- For \(x - 18 = -14\):
\[
x = -14 + 18 = 4
\]

3. Thus, the solutions are:
\[
\{32, 4\}
\]

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