Answer:
The solution to the quadratic equations are:
[tex]x=-2+2i,\:x=-2-2i[/tex]
Step-by-step explanation:
Consider the provided quadratic equation.
[tex]x^2 + 4x + 8 = 0[/tex]
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Substitute a=1, b=4 and c=8 in above formula.
[tex]x_{1,\:2}=\frac{-4\pm \sqrt{4^2-4\cdot \:1\cdot \:8}}{2\cdot \:1}[/tex]
[tex]x_{1,\:2}=\frac{-4\pm \sqrt{16-32}}{2}[/tex]
[tex]x_{1,\:2}=\frac{-4\pm \sqrt{-16}}{2}[/tex]
[tex]x_{1,\:2}=\frac{-4\pm 4i}{2}[/tex]
[tex]x_{1,\:2}=-2\pm 2i[/tex]
Hence, the solution to the quadratic equations are:
[tex]x=-2+2i,\:x=-2-2i[/tex]
