x^2+(p+i)x+(q-5i)=0

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Solution for x^2+(p+i)x+(q-5i)=0 equation: 


Simplifying
x2 + (p + i) * x + (q + -5i) = 0

Reorder the terms:
x2 + (i + p) * x + (q + -5i) = 0

Reorder the terms for easier multiplication:
x2 + x(i + p) + (q + -5i) = 0
x2 + (i * x + p * x) + (q + -5i) = 0
x2 + (ix + px) + (q + -5i) = 0

Reorder the terms:
x2 + ix + px + (-5i + q) = 0

Remove parenthesis around (-5i + q)
x2 + ix + px + -5i + q = 0

Reorder the terms:
-5i + ix + px + q + x2 = 0

Solving
-5i + ix + px + q + x2 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-1px' to each side of the equation.
-5i + ix + px + q + -1px + x2 = 0 + -1px

Reorder the terms:
-5i + ix + px + -1px + q + x2 = 0 + -1px

Combine like terms: px + -1px = 0
-5i + ix + 0 + q + x2 = 0 + -1px
-5i + ix + q + x2 = 0 + -1px
Remove the zero:
-5i + ix + q + x2 = -1px

Add '-1q' to each side of the equation.
-5i + ix + q + -1q + x2 = -1px + -1q

Combine like terms: q + -1q = 0
-5i + ix + 0 + x2 = -1px + -1q
-5i + ix + x2 = -1px + -1q

Add '-1x2' to each side of the equation.
-5i + ix + x2 + -1x2 = -1px + -1q + -1x2

Combine like terms: x2 + -1x2 = 0
-5i + ix + 0 = -1px + -1q + -1x2
-5i + ix = -1px + -1q + -1x2

Reorder the terms:
-5i + ix + px + q + x2 = -1px + px + -1q + q + -1x2 + x2

Combine like terms: -1px + px = 0
-5i + ix + px + q + x2 = 0 + -1q + q + -1x2 + x2
-5i + ix + px + q + x2 = -1q + q + -1x2 + x2

Combine like terms: -1q + q = 0
-5i + ix + px + q + x2 = 0 + -1x2 + x2
-5i + ix + px + q + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-5i + ix + px + q + x2 = 0

The solution to this equation could not be determined.

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