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

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

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

{214,−178}

Answer 1

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

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

Calculating the square root of 196 gives us:

\[ \sqrt{196} = 14 \]

So, we have two cases:

1. \(x - 18 = 14\)
2. \(x - 18 = -14\)

Now, we solve each case:

1. Case 1: \[ x - 18 = 14 \] Adding 18 to both sides: \[ x = 14 + 18 = 32 \]

2. Case 2: \[ x - 18 = -14 \] Adding 18 to both sides: \[ x = -14 + 18 = 4 \]

Thus, the solutions are:

\[ {32, 4} \]

Therefore, the correct response is \({32, 4}\).