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

Question

.(1 point)
Responses

{53,19}
left brace 53 comma 19 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

{−19,−53}

Answer 1

To solve the quadratic equation \((x + 36)^2 - 38 = 251\), let's first isolate the term with the square.

1. Add 38 to both sides:

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

2. Next, take the square root of both sides:

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

3. Now, we solve for \(x\) in two cases:

Case 1: \(x + 36 = 17\)

\[ x = 17 - 36 \] \[ x = -19 \]

Case 2: \(x + 36 = -17\)

\[ x = -17 - 36 \] \[ x = -53 \]

4. Therefore, the solutions to the equation are:

\[ x = -19 \quad \text{and} \quad x = -53 \]

The final solution set is:

\[ {-19, -53} \]

So, the correct response is:

\({-19, -53}\)