(x-7-5i)(x-7+5i)=(x^2-14x+74)

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Solution for (x-7-5i)(x-7+5i)=(x^2-14x+74) equation: 


Simplifying
(x + -7 + -5i)(x + -7 + 5i) = (x2 + -14x + 74)

Reorder the terms:
(-7 + -5i + x)(x + -7 + 5i) = (x2 + -14x + 74)

Reorder the terms:
(-7 + -5i + x)(-7 + 5i + x) = (x2 + -14x + 74)

Multiply (-7 + -5i + x) * (-7 + 5i + x)
(-7(-7 + 5i + x) + -5i * (-7 + 5i + x) + x(-7 + 5i + x)) = (x2 + -14x + 74)
((-7 * -7 + 5i * -7 + x * -7) + -5i * (-7 + 5i + x) + x(-7 + 5i + x)) = (x2 + -14x + 74)
((49 + -35i + -7x) + -5i * (-7 + 5i + x) + x(-7 + 5i + x)) = (x2 + -14x + 74)
(49 + -35i + -7x + (-7 * -5i + 5i * -5i + x * -5i) + x(-7 + 5i + x)) = (x2 + -14x + 74)

Reorder the terms:
(49 + -35i + -7x + (35i + -5ix + -25i2) + x(-7 + 5i + x)) = (x2 + -14x + 74)
(49 + -35i + -7x + (35i + -5ix + -25i2) + x(-7 + 5i + x)) = (x2 + -14x + 74)
(49 + -35i + -7x + 35i + -5ix + -25i2 + (-7 * x + 5i * x + x * x)) = (x2 + -14x + 74)

Reorder the terms:
(49 + -35i + -7x + 35i + -5ix + -25i2 + (5ix + -7x + x2)) = (x2 + -14x + 74)
(49 + -35i + -7x + 35i + -5ix + -25i2 + (5ix + -7x + x2)) = (x2 + -14x + 74)

Reorder the terms:
(49 + -35i + 35i + -5ix + 5ix + -25i2 + -7x + -7x + x2) = (x2 + -14x + 74)

Combine like terms: -35i + 35i = 0
(49 + 0 + -5ix + 5ix + -25i2 + -7x + -7x + x2) = (x2 + -14x + 74)
(49 + -5ix + 5ix + -25i2 + -7x + -7x + x2) = (x2 + -14x + 74)

Combine like terms: -5ix + 5ix = 0
(49 + 0 + -25i2 + -7x + -7x + x2) = (x2 + -14x + 74)
(49 + -25i2 + -7x + -7x + x2) = (x2 + -14x + 74)

Combine like terms: -7x + -7x = -14x
(49 + -25i2 + -14x + x2) = (x2 + -14x + 74)

Reorder the terms:
49 + -25i2 + -14x + x2 = (74 + -14x + x2)

Remove parenthesis around (74 + -14x + x2)
49 + -25i2 + -14x + x2 = 74 + -14x + x2

Add '14x' to each side of the equation.
49 + -25i2 + -14x + 14x + x2 = 74 + -14x + 14x + x2

Combine like terms: -14x + 14x = 0
49 + -25i2 + 0 + x2 = 74 + -14x + 14x + x2
49 + -25i2 + x2 = 74 + -14x + 14x + x2

Combine like terms: -14x + 14x = 0
49 + -25i2 + x2 = 74 + 0 + x2
49 + -25i2 + x2 = 74 + x2

Add '-1x2' to each side of the equation.
49 + -25i2 + x2 + -1x2 = 74 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
49 + -25i2 + 0 = 74 + x2 + -1x2
49 + -25i2 = 74 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
49 + -25i2 = 74 + 0
49 + -25i2 = 74

Solving
49 + -25i2 = 74

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 + -49 + -25i2 = 74 + -49

Combine like terms: 49 + -49 = 0
0 + -25i2 = 74 + -49
-25i2 = 74 + -49

Combine like terms: 74 + -49 = 25
-25i2 = 25

Divide each side by '-25'.
i2 = -1

Simplifying
i2 = -1

Reorder the terms:
1 + i2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + i2 = 0

The solution to this equation could not be determined.

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