Answer:
[tex]x_{1} =-4+\sqrt{2} \\x_{2} =-4-\sqrt{2} \\[/tex]
Step-by-step explanation:
Using quadratic formula:
[tex]\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a}[/tex]
We will have 2 solutions.
x^2+8x+16=2
x^2+8x+14=0
a= 1 b=8 c= 14
[tex]x_{1}= \frac{-8+\sqrt{8^{2}-4*1*14} }{2*1} \\\\x_{2}= \frac{-8-\sqrt{8^{2}-4*1*14} }{2*1} \\[/tex]
We can write:
[tex]x_{1}= \frac{-8+\sqrt{{64}-56} }{2} \\\\x_{2}= \frac{-8-\sqrt{{64}-56} }{2} \\[/tex]
[tex]x_{1}= -4+\frac{\sqrt{{64}-56} }{2} \\\\x_{2}= -4-\frac{\sqrt{{64}-56} }{2} \\[/tex]
so, we have:
[tex]x_{1}= -4+\frac{\sqrt{{}8} }{2} \\\\x_{2}=-4-\frac{\sqrt{{}8} }{2} \\[/tex]
simplifying we have:
[tex]x_{1}= -4+\frac{\sqrt{{}2*4} }{2} \\\\x_{2}= -4-\frac{\sqrt{{}2*4} }{2} \\[/tex]
Finally:
[tex]x_{1}= -4+\sqrt{2} \\\\x_{2}= -4-\sqrt{2} \\[/tex]
