4v^2 + 6 v + 8 = 0. v=? (Enter your answer in the form a + bi. Thank you!

Answer 1

This is a quadratic equation, and it can be solved by completing the square or by using the Quadratic Formula.

Using the Quadratic Formula,

x= [-b +√(b²-4ac)] / (2a)

were for this equation, a=4, b=6, and c=8.

x=[-6 + √(36 – (4)(4)(8))] / (2)(4)

x=[-6 + √(36 – 128)]/8

x=[-6 + √(–92)]/8

√(-92) = √(-1)·√(92) = i ·2√23 SO...

x = [ –6 + 2 i √23]/8

which simplifies to

x = -3/4 + ( i √23 ) / 4 or each answer is

x = –3/4 – (i √23)/4 and

x = –3/4 + i √23)/4