What are the solutions of 3x2 + 15 = –6x?

a) –1 ± i
b) –1 ± 2i
c) –2 ± i
d) –2 ± 2i

B) –1 ± 2i

Step-by-step explanation:

The equation; 3x² + 15 = –6x

Could be written as

3x²-6x + 15 = 0

Using the quadratic formula to solve for x

x = (-6 ± √(6²-4×3×15))/(2×3)

  = (-6 ± √(36 - 180))/6

  =  (-6 ± √(-144))/6

but √-1 = i

Therefore;

   =  (-6 ± √(144)i)/6

   = (-6 ± 12i)/6

  = -1 ± 2i

Choice B is the answer.

Step-by-step explanation:

We have given a quadratic equation.

3x² + 15 = –6x

3x²+6x+15  = 0

We have to find the solution of above equation.

Taking 3 common from above expression, we have

3(x²+2x+5)  =  0

x²+2x+5  =  0

From above equation, a  = 1,b = 2 and c = 5

x  = (-b±√b²-4ac ) / 2a is quadratic formula to solve equations.

Putting values in above formula ,we have

x = (-2±√(2)²-4(1)(5) ) / 2(1)

x  =  (-2±√4-20 ) / 2

x  =  (-2±√-16) / 2

x  =  (-2±√-1√16) / 2                                      ∵ i  =  √-1

x  =  (-2±4i) / 2

x  =  2(-1±2i) / 2

x  =  -1±2i

Hence, the solution of given equation is -1±2i.

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