Question

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

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

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

{214,−178}
left brace 214 comma negative 178 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 the square root of 196:
\[
\sqrt{196} = 14
\]

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

4. Solve the first equation:
\[
x - 18 = 14 \implies x = 18 + 14 = 32
\]

5. Solve the second equation:
\[
x - 18 = -14 \implies x = 18 - 14 = 4
\]

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

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

The correct answer is:
\(\{32, 4\}\)