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Simplifying 5j2 + -7j + -7 = 0 Reorder the terms: -7 + -7j + 5j2 = 0 Solving -7 + -7j + 5j2 = 0 Solving for variable 'j'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -1.4j + j2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -1.4j + 1.4 + j2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -1.4j + j2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -1.4j + j2 = 0 + 1.4 -1.4j + j2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -1.4j + j2 = 1.4 The j term is -1.4j. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4j + 0.49 + j2 = 1.4 + 0.49 Reorder the terms: 0.49 + -1.4j + j2 = 1.4 + 0.49 Combine like terms: 1.4 + 0.49 = 1.89 0.49 + -1.4j + j2 = 1.89 Factor a perfect square on the left side: (j + -0.7)(j + -0.7) = 1.89 Calculate the square root of the right side: 1.374772708 Break this problem into two subproblems by setting (j + -0.7) equal to 1.374772708 and -1.374772708.Subproblem 1
j + -0.7 = 1.374772708 Simplifying j + -0.7 = 1.374772708 Reorder the terms: -0.7 + j = 1.374772708 Solving -0.7 + j = 1.374772708 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + j = 1.374772708 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + j = 1.374772708 + 0.7 j = 1.374772708 + 0.7 Combine like terms: 1.374772708 + 0.7 = 2.074772708 j = 2.074772708 Simplifying j = 2.074772708Subproblem 2
j + -0.7 = -1.374772708 Simplifying j + -0.7 = -1.374772708 Reorder the terms: -0.7 + j = -1.374772708 Solving -0.7 + j = -1.374772708 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + j = -1.374772708 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + j = -1.374772708 + 0.7 j = -1.374772708 + 0.7 Combine like terms: -1.374772708 + 0.7 = -0.674772708 j = -0.674772708 Simplifying j = -0.674772708Solution
The solution to the problem is based on the solutions from the subproblems. j = {2.074772708, -0.674772708}
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