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

Question

Responses

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

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

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

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

Answer 1

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

1. Isolate the squared term: \[ (x + 36)^2 - 38 = 251 \] 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 \( \sqrt{289} = 17 \): \[ x + 36 = \pm 17 \]

3. Solve for \(x\):

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

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

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

Thus, the answer is: \[ {−19,−53} \]