(x-7+4i)(x-7-4i)=0

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Solution for (x-7+4i)(x-7-4i)=0 equation: 


Simplifying
(x + -7 + 4i)(x + -7 + -4i) = 0

Reorder the terms:
(-7 + 4i + x)(x + -7 + -4i) = 0

Reorder the terms:
(-7 + 4i + x)(-7 + -4i + x) = 0

Multiply (-7 + 4i + x) * (-7 + -4i + x)
(-7(-7 + -4i + x) + 4i * (-7 + -4i + x) + x(-7 + -4i + x)) = 0
((-7 * -7 + -4i * -7 + x * -7) + 4i * (-7 + -4i + x) + x(-7 + -4i + x)) = 0
((49 + 28i + -7x) + 4i * (-7 + -4i + x) + x(-7 + -4i + x)) = 0
(49 + 28i + -7x + (-7 * 4i + -4i * 4i + x * 4i) + x(-7 + -4i + x)) = 0

Reorder the terms:
(49 + 28i + -7x + (-28i + 4ix + -16i2) + x(-7 + -4i + x)) = 0
(49 + 28i + -7x + (-28i + 4ix + -16i2) + x(-7 + -4i + x)) = 0
(49 + 28i + -7x + -28i + 4ix + -16i2 + (-7 * x + -4i * x + x * x)) = 0

Reorder the terms:
(49 + 28i + -7x + -28i + 4ix + -16i2 + (-4ix + -7x + x2)) = 0
(49 + 28i + -7x + -28i + 4ix + -16i2 + (-4ix + -7x + x2)) = 0

Reorder the terms:
(49 + 28i + -28i + 4ix + -4ix + -16i2 + -7x + -7x + x2) = 0

Combine like terms: 28i + -28i = 0
(49 + 0 + 4ix + -4ix + -16i2 + -7x + -7x + x2) = 0
(49 + 4ix + -4ix + -16i2 + -7x + -7x + x2) = 0

Combine like terms: 4ix + -4ix = 0
(49 + 0 + -16i2 + -7x + -7x + x2) = 0
(49 + -16i2 + -7x + -7x + x2) = 0

Combine like terms: -7x + -7x = -14x
(49 + -16i2 + -14x + x2) = 0

Solving
49 + -16i2 + -14x + x2 = 0

Solving for variable 'i'.

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

Add '-49' to each side of the equation.
49 + -16i2 + -14x + -49 + x2 = 0 + -49

Reorder the terms:
49 + -49 + -16i2 + -14x + x2 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + -16i2 + -14x + x2 = 0 + -49
-16i2 + -14x + x2 = 0 + -49

Combine like terms: 0 + -49 = -49
-16i2 + -14x + x2 = -49

Add '14x' to each side of the equation.
-16i2 + -14x + 14x + x2 = -49 + 14x

Combine like terms: -14x + 14x = 0
-16i2 + 0 + x2 = -49 + 14x
-16i2 + x2 = -49 + 14x

Add '-1x2' to each side of the equation.
-16i2 + x2 + -1x2 = -49 + 14x + -1x2

Combine like terms: x2 + -1x2 = 0
-16i2 + 0 = -49 + 14x + -1x2
-16i2 = -49 + 14x + -1x2

Divide each side by '-16'.
i2 = 3.0625 + -0.875x + 0.0625x2

Simplifying
i2 = 3.0625 + -0.875x + 0.0625x2

Reorder the terms:
-3.0625 + i2 + 0.875x + -0.0625x2 = 3.0625 + -0.875x + 0.0625x2 + -3.0625 + 0.875x + -0.0625x2

Reorder the terms:
-3.0625 + i2 + 0.875x + -0.0625x2 = 3.0625 + -3.0625 + -0.875x + 0.875x + 0.0625x2 + -0.0625x2

Combine like terms: 3.0625 + -3.0625 = 0.0000
-3.0625 + i2 + 0.875x + -0.0625x2 = 0.0000 + -0.875x + 0.875x + 0.0625x2 + -0.0625x2
-3.0625 + i2 + 0.875x + -0.0625x2 = -0.875x + 0.875x + 0.0625x2 + -0.0625x2

Combine like terms: -0.875x + 0.875x = 0.000
-3.0625 + i2 + 0.875x + -0.0625x2 = 0.000 + 0.0625x2 + -0.0625x2
-3.0625 + i2 + 0.875x + -0.0625x2 = 0.0625x2 + -0.0625x2

Combine like terms: 0.0625x2 + -0.0625x2 = 0.0000
-3.0625 + i2 + 0.875x + -0.0625x2 = 0.0000

The solution to this equation could not be determined.

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