Question

Solve the following quadratic equation using square roots: (x−18)exponent2=196 .(1 point)
Responses

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

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

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

{32,4}

Answer 1

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

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

2. **Calculate the square root of 196**:
\[
\sqrt{196} = 14
\]

3. **Set up the two equations**:
\[
x - 18 = 14 \quad \text{and} \quad x - 18 = -14
\]

4. **Solve for \(x\)** in each case:
- 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. **Write the solution set**:
\[
\{32, 4\}
\]

Thus, the correct response is:
\[
\{32, 4\}
\]