Solve the following quadratic equation using square roots: (x+36)2−38=251

Question

(
𝑥
+
36
)
2
−
38
=
251
.(1 point)
Responses

{17.84,−13.84}
{
17.84
,
−
13.84
}
left brace 17.84 comma negative 13.84 right brace

{253,−325}
{
253
,
−
325
}
left brace 253 comma negative 325 right brace

{−19,−53}
{
−
19
,
−
53
}
left brace negative 19 comma negative 53 right brace

{53,19}

Answer 1

To solve the quadratic equation \((x + 36)^2 - 38 = 251\) using square roots, follow these steps:

1. Isolate the squared term: \[ (x + 36)^2 - 38 = 251 \] Add 38 to both sides: \[ (x + 36)^2 = 251 + 38 \] \[ (x + 36)^2 = 289 \]

2. Take the square root of both sides: \[ x + 36 = \pm \sqrt{289} \]

   Since \(\sqrt{289} = 17\): \[ x + 36 = 17 \quad \text{or} \quad x + 36 = -17 \]

3. Solve for \(x\) in both cases:

   1. For \(x + 36 = 17\): \[ x = 17 - 36 \] \[ x = -19 \]

   2. For \(x + 36 = -17\): \[ x = -17 - 36 \] \[ x = -53 \]

4. The solutions are: \[ x = -19 \quad \text{and} \quad x = -53 \]

Therefore, the solution set is \({ -19, -53 }\).

The correct response is: \[ { -19, -53 } \]