Question

Solve the following quadratic equation using square roots: (x - 18)? = 196. (1 point)
0 (32,4}
0 {21,5}
• 1-4, -32}
• 1214, - 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. Now, set up two equations:
\[
x - 18 = 14 \quad \text{or} \quad x - 18 = -14
\]

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

5. The solutions are \(x = 32\) and \(x = 4\).

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

From the options provided, the correct answer is:
\[
\{32, 4\}
\]