Answer:
The correct answer is c.
Step-by-step explanation:
Given the equation
[tex]ax^{2}+bx+c=0[/tex]
The quadratic equation solves the values of ''x'' which satisfy the original equation (In the equation I replace ± by the symbol |):
[tex]\frac{-b|\sqrt{b^{2}-4ac}}{2a}[/tex]
The solutions of [tex]4x^{2}+x=-3[/tex] are the same that the solutions of [tex]4x^{2}+x+3=0[/tex]
With [tex]a=4\\b=1\\c=3[/tex] we replace this in the quadratic equation ⇒
[tex]\frac{-1|\sqrt{(1)^{2}-4(4)(3)}}{(2)(4)}[/tex] ⇒
[tex]\frac{-1|\sqrt{1-48}}{8}[/tex] ⇒
[tex]\frac{-1|\sqrt{-47}}{8}[/tex]
Given that [tex]i^{2}=-1[/tex] (imaginary numbers property)
[tex]\frac{-1|\sqrt{47i^{2}}}{8}=\frac{-1|i\sqrt{47}}{8}[/tex]
The solutions are [tex]\frac{-1+i\sqrt{47}}{8}[/tex]
and [tex]\frac{-1-i\sqrt{47}}{8}[/tex]
The correct answer is c.
