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

Question

.(1 point)
Responses

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

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

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

​ {−4,−32}

Answer 1

To solve the equation \((x - 18)^2 = 196\) using square roots, we start by taking the square root of both sides:

\[ x - 18 = \pm \sqrt{196} \]

Calculating \(\sqrt{196}\):

\[ \sqrt{196} = 14 \]

So, we have:

\[ x - 18 = 14 \quad \text{or} \quad x - 18 = -14 \]

We can solve these two equations separately.

1. For \(x - 18 = 14\):

\[ x = 14 + 18 = 32 \]

2. For \(x - 18 = -14\):

\[ x = -14 + 18 = 4 \]

Thus, the solutions to the equation are:

\[ {32, 4} \]

The correct response is:

\({32, 4}\)