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

Question

Responses

{−19,−53}
{17.84,−13.84}
{53,19}
{253,−325}

Answer 1

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

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

2. Now, take the square root of both sides: \[ x + 36 = \pm \sqrt{289} \] The square root of 289 is 17, so: \[ x + 36 = \pm 17 \]

3. We will consider both cases:

   Case 1: \[ x + 36 = 17 \] Subtracting 36 from both sides: \[ x = 17 - 36 \] \[ x = -19 \]

   Case 2: \[ x + 36 = -17 \] Subtracting 36 from both sides: \[ x = -17 - 36 \] \[ x = -53 \]

So the solutions to the equation are \(x = -19\) and \(x = -53\).

The correct response is: \({-19, -53}\)