Answer (Please vote me Brainliest if this helps!):
The solution is B.
Step-by-step explanation:
Solve with the quadratic formula
[tex]x_{1,\:2}=\frac{-\left(-7\right)\pm \sqrt{\left(-7\right)^2-4\cdot \:1\cdot \:13}}{2\cdot \:1}[/tex]
Simplify
[tex]x_{1,\:2}=\frac{-\left(-7\right)\pm \sqrt{3}i}{2\cdot \:1}[/tex]
Separate the solutions
[tex]x_1=\frac{-\left(-7\right)+\sqrt{3}i}{2\cdot \:1},\:x_2=\frac{-\left(-7\right)-\sqrt{3}i}{2\cdot \:1}[/tex]
[tex]\frac{-\left(-7\right)+\sqrt{3}i}{2\cdot \:1}[/tex]
Apply rule - (-a) = a
[tex]\frac{7+\sqrt{3}i}{2\cdot \:1}[/tex]
Multiply the numbers: 2 · 1 = 2
[tex]\frac{7+\sqrt{3}i}{2}[/tex]
[tex]\frac{-\left(-7\right)-\sqrt{3}i}{2\cdot \:1}[/tex]
Apply rule - (-a) = a
[tex]\frac{7-\sqrt{3}i}{2\cdot \:1}[/tex]
Multiply the numbers: 2 · 1 = 2
[tex]\frac{7-\sqrt{3}i}{2}[/tex]
The solutions to the quadratic equations are:
[tex]\frac{7+\sqrt{3}i}{2}[/tex], [tex]\frac{7-\sqrt{3}i}{2}[/tex]
