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

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

{214,−178}

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**:

\[
x - 18 = 14 \quad \text{or} \quad x - 18 = -14
\]

4. **Solve each equation**:

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

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

5. **List the solutions**:
The solutions to the equation are \(x = 32\) and \(x = 4\).

Thus, the solution set is \(\{32, 4\}\).

The correct response is:

\(\{32, 4\}\)
left brace 32 comma 4 right brace.