Question

Solve for x in the equation x ^ 2 + 2x + 1 = 17

O x = - 1 plus/minus sqrt(13)

O x = - 2 plus/minus 2 * sqrt(5)

O x = - 1 plus/minus sqrt(17)

O x = - 1 plus/minus sqrt(15)

Answer 1

Answer:

$x=-1+\sqrt{17},\:x=-1-\sqrt{17}$

Step-by-step explanation:

$x ^ 2 + 2x + 1 = 17$

$\mathrm{Subtract\:}17\mathrm{\:from\:both\:sides}$

$x^2+2x+1-17=17-17$

$\mathrm{Simplify}$

$x^2+2x-16=0$

$\mathrm{Solve\;with\;Quadratic\;formula}$

$x_{1,\:2}=\frac{-2\pm \sqrt{2^2-4\cdot \:1\cdot \left(-16\right)}}{2\cdot \:1}$

$\sqrt{2^2-4 \cdot1\cdot(-16)} =\sqrt[2]{17}$

$x_{1,\:2}=\frac{-2\pm \:2\sqrt{17}}{2\cdot \:1}$

$\mathrm{Separate\:the\:solutions}$

$x_1=\frac{-2+2\sqrt{17}}{2\cdot \:1},\:x_2=\frac{-2-2\sqrt{17}}{2\cdot \:1}$

$\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}$

$x=-1+\sqrt{17},\:x=-1-\sqrt{17}$

Hence, Answer is [C] $x=-1+\sqrt{17},\:x=-1-\sqrt{17}$

~Lenvy~