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Simplifying [x + -1(5i)][x + -1(5i)] = 0 Remove parenthesis around (5i) [x + -1 * 5i][x + -1(5i)] = 0 Multiply -1 * 5 [x + -5i][x + -1(5i)] = 0 Reorder the terms: [-5i + x][x + -1(5i)] = 0 Remove parenthesis around (5i) [-5i + x][x + -1 * 5i] = 0 Multiply -1 * 5 [-5i + x][x + -5i] = 0 Reorder the terms: [-5i + x][-5i + x] = 0 Multiply [-5i + x] * [-5i + x] [-5i * [-5i + x] + x[-5i + x]] = 0 [[-5i * -5i + x * -5i] + x[-5i + x]] = 0 Reorder the terms: [[-5ix + 25i2] + x[-5i + x]] = 0 [[-5ix + 25i2] + x[-5i + x]] = 0 [-5ix + 25i2 + [-5i * x + x * x]] = 0 [-5ix + 25i2 + [-5ix + x2]] = 0 Reorder the terms: [-5ix + -5ix + 25i2 + x2] = 0 Combine like terms: -5ix + -5ix = -10ix [-10ix + 25i2 + x2] = 0 Solving -10ix + 25i2 + x2 = 0 Solving for variable 'i'. Factor a trinomial. (5i + -1x)(5i + -1x) = 0Subproblem 1
Set the factor '(5i + -1x)' equal to zero and attempt to solve: Simplifying 5i + -1x = 0 Solving 5i + -1x = 0 Move all terms containing i to the left, all other terms to the right. Add 'x' to each side of the equation. 5i + -1x + x = 0 + x Combine like terms: -1x + x = 0 5i + 0 = 0 + x 5i = 0 + x Remove the zero: 5i = x Divide each side by '5'. i = 0.2x Simplifying i = 0.2xSubproblem 2
Set the factor '(5i + -1x)' equal to zero and attempt to solve: Simplifying 5i + -1x = 0 Solving 5i + -1x = 0 Move all terms containing i to the left, all other terms to the right. Add 'x' to each side of the equation. 5i + -1x + x = 0 + x Combine like terms: -1x + x = 0 5i + 0 = 0 + x 5i = 0 + x Remove the zero: 5i = x Divide each side by '5'. i = 0.2x Simplifying i = 0.2xSolution
i = {0.2x, 0.2x}
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