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

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

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

{−19,−53}

Answer 1

To solve the equation \((x + 36)^2 - 38 = 251\), we first isolate the squared term:

1. Add \(38\) to both sides of the equation: \[ (x + 36)^2 = 251 + 38 \] \[ (x + 36)^2 = 289 \]

2. Take the square root of both sides: \[ x + 36 = \pm \sqrt{289} \] Since \(\sqrt{289} = 17\), we have: \[ x + 36 = 17 \quad \text{or} \quad x + 36 = -17 \]

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

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

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

Thus the solutions are: \[ x = -19 \quad \text{and} \quad x = -53 \]

The answer is \({-19, -53}\).