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Simplifying (x + -7 + -5i)(x + -7 + 5i) = 0 Reorder the terms: (-7 + -5i + x)(x + -7 + 5i) = 0 Reorder the terms: (-7 + -5i + x)(-7 + 5i + x) = 0 Multiply (-7 + -5i + x) * (-7 + 5i + x) (-7(-7 + 5i + x) + -5i * (-7 + 5i + x) + x(-7 + 5i + x)) = 0 ((-7 * -7 + 5i * -7 + x * -7) + -5i * (-7 + 5i + x) + x(-7 + 5i + x)) = 0 ((49 + -35i + -7x) + -5i * (-7 + 5i + x) + x(-7 + 5i + x)) = 0 (49 + -35i + -7x + (-7 * -5i + 5i * -5i + x * -5i) + x(-7 + 5i + x)) = 0 Reorder the terms: (49 + -35i + -7x + (35i + -5ix + -25i2) + x(-7 + 5i + x)) = 0 (49 + -35i + -7x + (35i + -5ix + -25i2) + x(-7 + 5i + x)) = 0 (49 + -35i + -7x + 35i + -5ix + -25i2 + (-7 * x + 5i * x + x * x)) = 0 Reorder the terms: (49 + -35i + -7x + 35i + -5ix + -25i2 + (5ix + -7x + x2)) = 0 (49 + -35i + -7x + 35i + -5ix + -25i2 + (5ix + -7x + x2)) = 0 Reorder the terms: (49 + -35i + 35i + -5ix + 5ix + -25i2 + -7x + -7x + x2) = 0 Combine like terms: -35i + 35i = 0 (49 + 0 + -5ix + 5ix + -25i2 + -7x + -7x + x2) = 0 (49 + -5ix + 5ix + -25i2 + -7x + -7x + x2) = 0 Combine like terms: -5ix + 5ix = 0 (49 + 0 + -25i2 + -7x + -7x + x2) = 0 (49 + -25i2 + -7x + -7x + x2) = 0 Combine like terms: -7x + -7x = -14x (49 + -25i2 + -14x + x2) = 0 Solving 49 + -25i2 + -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 + -25i2 + -14x + -49 + x2 = 0 + -49 Reorder the terms: 49 + -49 + -25i2 + -14x + x2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -25i2 + -14x + x2 = 0 + -49 -25i2 + -14x + x2 = 0 + -49 Combine like terms: 0 + -49 = -49 -25i2 + -14x + x2 = -49 Add '14x' to each side of the equation. -25i2 + -14x + 14x + x2 = -49 + 14x Combine like terms: -14x + 14x = 0 -25i2 + 0 + x2 = -49 + 14x -25i2 + x2 = -49 + 14x Add '-1x2' to each side of the equation. -25i2 + x2 + -1x2 = -49 + 14x + -1x2 Combine like terms: x2 + -1x2 = 0 -25i2 + 0 = -49 + 14x + -1x2 -25i2 = -49 + 14x + -1x2 Divide each side by '-25'. i2 = 1.96 + -0.56x + 0.04x2 Simplifying i2 = 1.96 + -0.56x + 0.04x2 Reorder the terms: -1.96 + i2 + 0.56x + -0.04x2 = 1.96 + -0.56x + 0.04x2 + -1.96 + 0.56x + -0.04x2 Reorder the terms: -1.96 + i2 + 0.56x + -0.04x2 = 1.96 + -1.96 + -0.56x + 0.56x + 0.04x2 + -0.04x2 Combine like terms: 1.96 + -1.96 = 0.00 -1.96 + i2 + 0.56x + -0.04x2 = 0.00 + -0.56x + 0.56x + 0.04x2 + -0.04x2 -1.96 + i2 + 0.56x + -0.04x2 = -0.56x + 0.56x + 0.04x2 + -0.04x2 Combine like terms: -0.56x + 0.56x = 0.00 -1.96 + i2 + 0.56x + -0.04x2 = 0.00 + 0.04x2 + -0.04x2 -1.96 + i2 + 0.56x + -0.04x2 = 0.04x2 + -0.04x2 Combine like terms: 0.04x2 + -0.04x2 = 0.00 -1.96 + i2 + 0.56x + -0.04x2 = 0.00 The solution to this equation could not be determined.
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