solve for x in the equation $x^{2}+2x + 1=17$.\n$x=-1pmsqrt{15}$\n$x=-1pmsqrt{17}$\n$x=-2pm2sqrt{5}$\n$x=-1pm…

Explanation:

Step1: Recognize perfect - square trinomial

The left - hand side of the equation $x^{2}+2x + 1$ is a perfect - square trinomial, which can be factored as $(x + 1)^{2}$. So the equation becomes $(x + 1)^{2}=17$.

Step2: Take square root of both sides

Taking the square root of both sides, we get $x + 1=\pm\sqrt{17}$.

Step3: Solve for x

Subtract 1 from both sides: $x=-1\pm\sqrt{17}$.

Answer:

$x=-1\pm\sqrt{17}$, so the correct option is $x=-1\pm\sqrt{17}$ (the second option in the list).