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

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

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

{21,5}

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

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

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

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

So, the solutions to the original equation are \(\{32, 4\}\).

The correct response from your options is:
**{32, 4}**.