For this case we must solve the following quadratic equation:
[tex]x ^ 2 + 8x + 25 = 0[/tex]
We solve the equation using the quadratic formula:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
Where:
[tex]a = 1\\b = 8\\c = 25[/tex]
Substituting we have:
[tex]x = \frac {-8 \pm \sqrt {8 ^ 2-4 (1) (25)}} {2 (1)}\\x = \frac {-8 \pm \sqrt {64-100}} {2}\\x = \frac {-8 \pm \sqrt {-36}} {2}[/tex]
By definition we have that [tex]i ^ 2 = -1[/tex], then:
[tex]x = \frac {-8 \pm \sqrt {36i ^ 2}} {2}\\x = \frac {-8 \pmi \sqrt {36}} {2}\\x = \frac {-8 ± 6i} {2}\\x = -4 \pm3i[/tex]
We have two complex roots:
[tex]x_ {1} = - 4 + 3i\\x_ {2} = - 4-3i[/tex]
Answer:
[tex]x_ {1} = - 4 + 3i\\x_ {2} = - 4-3i[/tex]
