x² + 10x + 16 = 0
a = 1
b = 10
c = 16
∆ = b² - 4 . a . c
∆ = 10² - 4 . 1 . 16
∆ = 100 - 64
∆ = 36
x = - b ± √∆
------------
2a
x' = - 10 + 6
----------
2 . 1
x' = - 4
---
2
x' = - 2
x" = - 10 - 6
----------
2 . 1
x" = - 16
---
2
x" = - 8
S = {-2 , -8}
[tex] \large \boxed{ \begin{array}{l} \rm x {}^{2} + 10x + 16 = 0 \\ \\ \rm a = 1 \\ \rm b = 10 \\ \rm c = 16 \\ \\ \rm\Delta = {b}^{2} - 4ac \\ \rm \Delta = 10 {}^{2} - 4.1.16 \\ \rm \Delta = 100 - 64 \\ \rm\Delta = 36 \\ \\ \rm x = \dfrac{ - b \pm \sqrt{\Delta} }{2a} \\ \\ \rm x = \dfrac{ - 10 \pm \sqrt{36} }{2.1} \\ \\ \rm x = \dfrac{ - 10 \pm6}{2} \begin{cases} x_1 = \dfrac{ - 10 + 6}{2} = \dfrac{ - 4}{2} = - 2 \\ \\ \rm x_2 = \dfrac{ - 10 - 6}{2} = \dfrac{ - 16}{2} = - 8 \end{cases} \\ \\ \rm \: S = \{ - 2; - 8\} \end{array}}[/tex]
