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

Question

.(1 point)
Responses

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

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

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

{53,19}

Answer 1

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

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

2. Now, take the square root of both sides: \[ x + 36 = \pm \sqrt{289} \] The square root of 289 is 17, so: \[ x + 36 = 17 \quad \text{or} \quad x + 36 = -17 \]

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

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

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

4. Therefore, the solutions to the equation are: \[ x = -19 \quad \text{and} \quad x = -53 \]

The solution set is: \[ {-19, -53} \]

So the correct response is: \({-19, -53}\)