Answer:
[tex]x1=-0.25(+)(0.25i)[/tex]
[tex]x2=-0.25(-)(0.25i)[/tex]
Step-by-step explanation:
we have
[tex]8x^{2}+4x=-1[/tex]
Factor the leading coefficient
[tex]8(x^{2}+0.5x)=-1[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]8(x^{2}+0.5x+1/16)=-1+1/2[/tex]
[tex]8(x^{2}+0.5x+1/16)=-1/2[/tex]
[tex](x^{2}+0.5x+1/16)=-1/16[/tex]
Rewrite as perfect squares
[tex](x+0.25)^{2}=-1/16[/tex]
remember that
[tex]i=\sqrt{-1}[/tex]
[tex](x+0.25)=(+/-)(0.25i)[/tex]
[tex]x=-0.25(+/-)(0.25i)[/tex]
[tex]x1=-0.25(+)(0.25i)[/tex]
[tex]x2=-0.25(-)(0.25i)[/tex]
