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

Question

.(1 point)
Responses

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

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

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

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

Answer 1

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

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

Calculating the square root of 196 gives us:

\[ \sqrt{196} = 14 \]

So we have:

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

Now, we solve each equation 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:

\[ x = 32 \quad \text{and} \quad x = 4 \]

Putting this in set notation, the solution is:

\({32, 4}\)

The correct response is:

{32, 4}