Solve for x in the equation x2 + 14x+17--96x=-7+4/6;x=-7 + 8ix=7+4/6;x = 7 + 8i

Answer:Option B.Step-by-step explanation:If a quadratic equation is defined as [tex]ax^2+bx+c=0[/tex], the by quadratic formula[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]Consider the given equation is[tex]x^2+14x+17=-96[/tex]We need to find the value of x.Add 96 on both sides.[tex]x^2+14x+17+96=-96+96[/tex][tex]x^2+14x+113=0[/tex]Here, a=1, b=14 and c=113. Using quadratic formula we get[tex]x=\dfrac{-14\pm \sqrt{14^2-4(1)(113)}}{2(1)}[/tex][tex]x=\dfrac{-14\pm \sqrt{-256}}{2(1)}[/tex][tex]x=\dfrac{-14\pm \sqrt{256}\sqrt{-1}}{2}[/tex]           [tex](\sqrt{-1}=i)[/tex][tex]x=\dfrac{-14\pm 16i}{2}[/tex][tex]x=-7\pm 8i[/tex]The value of x are x=-7 + 8i and x=-7 - 8i.Therefore, the correct option is B.