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Simplifying [x + -1(2 + -5i)][x + -1(2 + 5i)] = y [x + (2 * -1 + -5i * -1)][x + -1(2 + 5i)] = y [x + (-2 + 5i)][x + -1(2 + 5i)] = y Reorder the terms: [-2 + 5i + x][x + -1(2 + 5i)] = y [-2 + 5i + x][x + (2 * -1 + 5i * -1)] = y [-2 + 5i + x][x + (-2 + -5i)] = y Reorder the terms: [-2 + 5i + x][-2 + -5i + x] = y Multiply [-2 + 5i + x] * [-2 + -5i + x] [-2[-2 + -5i + x] + 5i * [-2 + -5i + x] + x[-2 + -5i + x]] = y [[-2 * -2 + -5i * -2 + x * -2] + 5i * [-2 + -5i + x] + x[-2 + -5i + x]] = y [[4 + 10i + -2x] + 5i * [-2 + -5i + x] + x[-2 + -5i + x]] = y [4 + 10i + -2x + [-2 * 5i + -5i * 5i + x * 5i] + x[-2 + -5i + x]] = y Reorder the terms: [4 + 10i + -2x + [-10i + 5ix + -25i2] + x[-2 + -5i + x]] = y [4 + 10i + -2x + [-10i + 5ix + -25i2] + x[-2 + -5i + x]] = y [4 + 10i + -2x + -10i + 5ix + -25i2 + [-2 * x + -5i * x + x * x]] = y Reorder the terms: [4 + 10i + -2x + -10i + 5ix + -25i2 + [-5ix + -2x + x2]] = y [4 + 10i + -2x + -10i + 5ix + -25i2 + [-5ix + -2x + x2]] = y Reorder the terms: [4 + 10i + -10i + 5ix + -5ix + -25i2 + -2x + -2x + x2] = y Combine like terms: 10i + -10i = 0 [4 + 0 + 5ix + -5ix + -25i2 + -2x + -2x + x2] = y [4 + 5ix + -5ix + -25i2 + -2x + -2x + x2] = y Combine like terms: 5ix + -5ix = 0 [4 + 0 + -25i2 + -2x + -2x + x2] = y [4 + -25i2 + -2x + -2x + x2] = y Combine like terms: -2x + -2x = -4x [4 + -25i2 + -4x + x2] = y Solving 4 + -25i2 + -4x + x2 = y Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -25i2 + -4x + -4 + x2 = -4 + y Reorder the terms: 4 + -4 + -25i2 + -4x + x2 = -4 + y Combine like terms: 4 + -4 = 0 0 + -25i2 + -4x + x2 = -4 + y -25i2 + -4x + x2 = -4 + y Add '4x' to each side of the equation. -25i2 + -4x + 4x + x2 = -4 + 4x + y Combine like terms: -4x + 4x = 0 -25i2 + 0 + x2 = -4 + 4x + y -25i2 + x2 = -4 + 4x + y Add '-1x2' to each side of the equation. -25i2 + x2 + -1x2 = -4 + 4x + -1x2 + y Combine like terms: x2 + -1x2 = 0 -25i2 + 0 = -4 + 4x + -1x2 + y -25i2 = -4 + 4x + -1x2 + y Divide each side by '-25'. i2 = 0.16 + -0.16x + 0.04x2 + -0.04y Simplifying i2 = 0.16 + -0.16x + 0.04x2 + -0.04y Reorder the terms: -0.16 + i2 + 0.16x + -0.04x2 + 0.04y = 0.16 + -0.16x + 0.04x2 + -0.04y + -0.16 + 0.16x + -0.04x2 + 0.04y Reorder the terms: -0.16 + i2 + 0.16x + -0.04x2 + 0.04y = 0.16 + -0.16 + -0.16x + 0.16x + 0.04x2 + -0.04x2 + -0.04y + 0.04y Combine like terms: 0.16 + -0.16 = 0.00 -0.16 + i2 + 0.16x + -0.04x2 + 0.04y = 0.00 + -0.16x + 0.16x + 0.04x2 + -0.04x2 + -0.04y + 0.04y -0.16 + i2 + 0.16x + -0.04x2 + 0.04y = -0.16x + 0.16x + 0.04x2 + -0.04x2 + -0.04y + 0.04y Combine like terms: -0.16x + 0.16x = 0.00 -0.16 + i2 + 0.16x + -0.04x2 + 0.04y = 0.00 + 0.04x2 + -0.04x2 + -0.04y + 0.04y -0.16 + i2 + 0.16x + -0.04x2 + 0.04y = 0.04x2 + -0.04x2 + -0.04y + 0.04y Combine like terms: 0.04x2 + -0.04x2 = 0.00 -0.16 + i2 + 0.16x + -0.04x2 + 0.04y = 0.00 + -0.04y + 0.04y -0.16 + i2 + 0.16x + -0.04x2 + 0.04y = -0.04y + 0.04y Combine like terms: -0.04y + 0.04y = 0.00 -0.16 + i2 + 0.16x + -0.04x2 + 0.04y = 0.00 The solution to this equation could not be determined.
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