Question

Solve the following quadratic equation using square roots: (x−18)2=196 .(1 point)
Responses

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

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

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

​ {−4,−32}

Answer 1

To solve the 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 the square root of 196:
\[
\sqrt{196} = 14
\]

3. Now, we have two equations to solve:
\[
x - 18 = 14
\]
\[
x - 18 = -14
\]

4. Solve for \(x\) in both cases:
- For \(x - 18 = 14\):
\[
x = 14 + 18 = 32
\]
- For \(x - 18 = -14\):
\[
x = -14 + 18 = 4
\]

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

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

The correct answer is:
\(\{32, 4\}\) (left brace 32 comma 4 right brace).