Question

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

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

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

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

{32,4}

Answer 1

To solve the equation \((x-18)^2 = 196\) using square roots, we 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, we have two equations to solve:
\[
x - 18 = 14 \quad \text{and} \quad x - 18 = -14
\]

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

5. For the second equation:
\[
x - 18 = -14
\]
\[
x = -14 + 18
\]
\[
x = 4
\]

Thus, the solutions to the equation are:
\[
\{32, 4\}
\]

So the correct response is:
\(\{32, 4\}\)