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 equation \((x - 18)^2 = 196\), we can use the square root method.

1. First, we take the square root of both sides:
\[
x - 18 = \pm \sqrt{196}
\]

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

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

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

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

Thus, the solutions to the quadratic equation \((x - 18)^2 = 196\) are:
\[
\{32, 4\}
\]

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