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Simplifying 2.7 = 10I + -7I2 Solving 2.7 = 10I + -7I2 Solving for variable 'I'. Reorder the terms: 2.7 + -10I + 7I2 = 10I + -10I + -7I2 + 7I2 Combine like terms: 10I + -10I = 0 2.7 + -10I + 7I2 = 0 + -7I2 + 7I2 2.7 + -10I + 7I2 = -7I2 + 7I2 Combine like terms: -7I2 + 7I2 = 0 2.7 + -10I + 7I2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.3857142857 + -1.428571429I + I2 = 0 Move the constant term to the right: Add '-0.3857142857' to each side of the equation. 0.3857142857 + -1.428571429I + -0.3857142857 + I2 = 0 + -0.3857142857 Reorder the terms: 0.3857142857 + -0.3857142857 + -1.428571429I + I2 = 0 + -0.3857142857 Combine like terms: 0.3857142857 + -0.3857142857 = 0.0000000000 0.0000000000 + -1.428571429I + I2 = 0 + -0.3857142857 -1.428571429I + I2 = 0 + -0.3857142857 Combine like terms: 0 + -0.3857142857 = -0.3857142857 -1.428571429I + I2 = -0.3857142857 The I term is -1.428571429I. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429I + 0.5102040819 + I2 = -0.3857142857 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429I + I2 = -0.3857142857 + 0.5102040819 Combine like terms: -0.3857142857 + 0.5102040819 = 0.1244897962 0.5102040819 + -1.428571429I + I2 = 0.1244897962 Factor a perfect square on the left side: (I + -0.7142857145)(I + -0.7142857145) = 0.1244897962 Calculate the square root of the right side: 0.352831116 Break this problem into two subproblems by setting (I + -0.7142857145) equal to 0.352831116 and -0.352831116.Subproblem 1
I + -0.7142857145 = 0.352831116 Simplifying I + -0.7142857145 = 0.352831116 Reorder the terms: -0.7142857145 + I = 0.352831116 Solving -0.7142857145 + I = 0.352831116 Solving for variable 'I'. Move all terms containing I to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + I = 0.352831116 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + I = 0.352831116 + 0.7142857145 I = 0.352831116 + 0.7142857145 Combine like terms: 0.352831116 + 0.7142857145 = 1.0671168305 I = 1.0671168305 Simplifying I = 1.0671168305Subproblem 2
I + -0.7142857145 = -0.352831116 Simplifying I + -0.7142857145 = -0.352831116 Reorder the terms: -0.7142857145 + I = -0.352831116 Solving -0.7142857145 + I = -0.352831116 Solving for variable 'I'. Move all terms containing I to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + I = -0.352831116 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + I = -0.352831116 + 0.7142857145 I = -0.352831116 + 0.7142857145 Combine like terms: -0.352831116 + 0.7142857145 = 0.3614545985 I = 0.3614545985 Simplifying I = 0.3614545985Solution
The solution to the problem is based on the solutions from the subproblems. I = {1.0671168305, 0.3614545985}
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