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

Question

Responses

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

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

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

{53,19}

Answer 1

To solve the quadratic equation \((x+36)^2 - 38 = 251\), we start by isolating the squared term.

1. 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 \(\sqrt{289} = 17\), we have: \[ x + 36 = \pm 17 \]

3. Solve for \(x\) in the two cases:

   • Case 1: \(x + 36 = 17\) \[ x = 17 - 36 = -19 \]

   • Case 2: \(x + 36 = -17\) \[ x = -17 - 36 = -53 \]

Thus, the solutions to the equation are: \[ { -19, -53 } \]

Therefore, the correct response is:

\({ -19, -53 }\)