Solve the following quadratic equation using square roots: (x+36)2−38=251 .(1 point)

Question

Responses

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

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

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

{253,−325}

Answer 1

To solve the equation \((x + 36)^2 - 38 = 251\), we can follow these steps:

1. Isolate the squared term:

   \[ (x + 36)^2 - 38 = 251 \] \[ (x + 36)^2 = 251 + 38 \] \[ (x + 36)^2 = 289 \]

2. Take square roots of both sides:

   \[ x + 36 = \pm \sqrt{289} \] \[ x + 36 = \pm 17 \]

3. Solve for \(x\):

   • For the positive case: \[ x + 36 = 17 \] \[ x = 17 - 36 \] \[ x = -19 \]

   • For the negative case: \[ x + 36 = -17 \] \[ x = -17 - 36 \] \[ x = -53 \]

So, the solutions to the equation are:

\[ { -19, -53 } \]

Thus, the correct response is:

\({ -19, -53 }\)