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Simplifying 3j2 + -20j = 12 Reorder the terms: -20j + 3j2 = 12 Solving -20j + 3j2 = 12 Solving for variable 'j'. Reorder the terms: -12 + -20j + 3j2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -20j + 3j2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + -6.666666667j + j2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -6.666666667j + 4 + j2 = 0 + 4 Reorder the terms: -4 + 4 + -6.666666667j + j2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -6.666666667j + j2 = 0 + 4 -6.666666667j + j2 = 0 + 4 Combine like terms: 0 + 4 = 4 -6.666666667j + j2 = 4 The j term is -6.666666667j. Take half its coefficient (-3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. -6.666666667j + 11.11111112 + j2 = 4 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667j + j2 = 4 + 11.11111112 Combine like terms: 4 + 11.11111112 = 15.11111112 11.11111112 + -6.666666667j + j2 = 15.11111112 Factor a perfect square on the left side: (j + -3.333333334)(j + -3.333333334) = 15.11111112 Calculate the square root of the right side: 3.887301264 Break this problem into two subproblems by setting (j + -3.333333334) equal to 3.887301264 and -3.887301264.Subproblem 1
j + -3.333333334 = 3.887301264 Simplifying j + -3.333333334 = 3.887301264 Reorder the terms: -3.333333334 + j = 3.887301264 Solving -3.333333334 + j = 3.887301264 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + j = 3.887301264 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + j = 3.887301264 + 3.333333334 j = 3.887301264 + 3.333333334 Combine like terms: 3.887301264 + 3.333333334 = 7.220634598 j = 7.220634598 Simplifying j = 7.220634598Subproblem 2
j + -3.333333334 = -3.887301264 Simplifying j + -3.333333334 = -3.887301264 Reorder the terms: -3.333333334 + j = -3.887301264 Solving -3.333333334 + j = -3.887301264 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + j = -3.887301264 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + j = -3.887301264 + 3.333333334 j = -3.887301264 + 3.333333334 Combine like terms: -3.887301264 + 3.333333334 = -0.55396793 j = -0.55396793 Simplifying j = -0.55396793Solution
The solution to the problem is based on the solutions from the subproblems. j = {7.220634598, -0.55396793}
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