Solve the following quadratic equation using square roots: (x+36)2−38=251 .(1 point) Responses {−19,−53} left brace negative 19 comma negative 53 right brace {53,19} left brace 53 comma 19 right brace {253,−325} left brace 253 comma negative 325 right brace {17.84,−13.84}

Answer 1

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

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

2. Take the square root of both sides: \[ x + 36 = \pm \sqrt{289} \] \[ x + 36 = \pm 17 \]

3. Solve for \(x\) by subtracting 36 from both sides.

For the positive square root: \[ x + 36 = 17 \] \[ x = 17 - 36 \] \[ x = -19 \]

For the negative square root: \[ x + 36 = -17 \] \[ x = -17 - 36 \] \[ x = -53 \]

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

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