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

Question

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

Answer 1

To solve the quadratic equation \((x+36)^2 - 38 = 251\), we can 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 \(\sqrt{289} = 17\): \[ x + 36 = 17 \quad \text{or} \quad x + 36 = -17 \]

3. Solve for \(x\): For the first equation: \[ x + 36 = 17 \] Subtract 36 from both sides: \[ x = 17 - 36 \] \[ x = -19 \]

   For the second equation: \[ x + 36 = -17 \] Subtract 36 from both sides: \[ x = -17 - 36 \] \[ x = -53 \]

4. Final solutions: The solutions to the equation are: \[ x = -19 \quad \text{and} \quad x = -53 \]

So the answer is: \({−19,−53}\)