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 of the equation:
\[
x - 18 = \pm \sqrt{196}
\]

2. Calculate the square root of 196:
\[
\sqrt{196} = 14
\]
So we have:
\[
x - 18 = 14 \quad \text{or} \quad x - 18 = -14
\]

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

Thus, the solutions to the equation are \(x = 32\) and \(x = 4\).

The answer is:
\[
\{32, 4\}
\]

So the response is:
\(\{32, 4\}\) left brace 32 comma 4 right brace.