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

Question

.(1 point)
Responses

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

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

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

{17.84,−13.84}

Answer 1

To solve the quadratic equation \((x+36)^2 - 38 = 251\), we will first simplify and isolate the square.

1. Start by adding 38 to both sides:

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

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

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

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

Since \(\sqrt{289} = 17\):

\[ x + 36 = \pm 17 \]

3. Now we will split this into two equations:

4. \(x + 36 = 17\)

5. \(x + 36 = -17\)

6. Solve the first equation:

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

5. Solve the second equation:

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

6. Therefore, the solutions to the equation are:

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

Thus, the final answer is:

\({-19, -53}\)

So the correct response is:

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