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