Question

Solve the following quadratic equation using square roots: (x−18) to the second power = 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 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 \(\sqrt{196}\):
\[
\sqrt{196} = 14
\]

3. This gives us two equations:
\[
x - 18 = 14 \quad \text{and} \quad x - 18 = -14
\]

4. Solve for \(x\) in each equation:
- For the first equation:
\[
x - 18 = 14 \implies x = 14 + 18 = 32
\]
- For the second equation:
\[
x - 18 = -14 \implies x = -14 + 18 = 4
\]

5. The solutions are:
\[
x = 32 \quad \text{and} \quad x = 4
\]

Thus, the solution set is:
\[
\{32, 4\}
\]

The correct response is:

**{32, 4}**