For this case we have the following equation:
[tex]x ^ 2 + 10x + 25 = 8\\x ^ 2 + 10x + 25-8 = 0\\x ^ 2 + 10x + 17 = 0[/tex]
We apply the quadratic formula:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
In this case we have:[tex]a = 1\\b = 10\\c = 17[/tex]
Substituting we have:
[tex]x = \frac {-10 \pm \sqrt {10 ^ 2-4 (1) (17)}} {2 (1)}\\x = \frac {-10 \pm \sqrt {100-68}} {2}\\x = \frac {-10 \pm \sqrt {32}} {2}\\x = \frac {-10 \pm \sqrt {4 ^ 2 * 2}} {2}\\x = \frac {-10 \pm4 \sqrt {2}} {2}[/tex]
We have two solutions:
[tex]x_ {1} = - 5 + 2 \sqrt {2}\\x_ {2} = - 5-2 \sqrt {2}[/tex]
Answer:
Option D, E
