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

{32,4}
left brace 32 comma 4 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, follow these steps:

1. Take the square root of both sides of the equation:
\[
x - 18 = \pm \sqrt{196}
\]

2. Calculate \(\sqrt{196}\):
\[
\sqrt{196} = 14
\]

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

4. Solve each equation for \(x\):

- For \(x - 18 = 14\):
\[
x = 14 + 18 = 32
\]

- For \(x - 18 = -14\):
\[
x = -14 + 18 = 4
\]

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

6. Therefore, the solution set is:
\[
\{32, 4\}
\]

The correct response is:
\(\{32, 4\}\)