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Simplifying 4j2 + 2j + -3 = 0 Reorder the terms: -3 + 2j + 4j2 = 0 Solving -3 + 2j + 4j2 = 0 Solving for variable 'j'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 0.5j + j2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 0.5j + 0.75 + j2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 0.5j + j2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 0.5j + j2 = 0 + 0.75 0.5j + j2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 0.5j + j2 = 0.75 The j term is 0.5j. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5j + 0.0625 + j2 = 0.75 + 0.0625 Reorder the terms: 0.0625 + 0.5j + j2 = 0.75 + 0.0625 Combine like terms: 0.75 + 0.0625 = 0.8125 0.0625 + 0.5j + j2 = 0.8125 Factor a perfect square on the left side: (j + 0.25)(j + 0.25) = 0.8125 Calculate the square root of the right side: 0.901387819 Break this problem into two subproblems by setting (j + 0.25) equal to 0.901387819 and -0.901387819.Subproblem 1
j + 0.25 = 0.901387819 Simplifying j + 0.25 = 0.901387819 Reorder the terms: 0.25 + j = 0.901387819 Solving 0.25 + j = 0.901387819 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + j = 0.901387819 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + j = 0.901387819 + -0.25 j = 0.901387819 + -0.25 Combine like terms: 0.901387819 + -0.25 = 0.651387819 j = 0.651387819 Simplifying j = 0.651387819Subproblem 2
j + 0.25 = -0.901387819 Simplifying j + 0.25 = -0.901387819 Reorder the terms: 0.25 + j = -0.901387819 Solving 0.25 + j = -0.901387819 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + j = -0.901387819 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + j = -0.901387819 + -0.25 j = -0.901387819 + -0.25 Combine like terms: -0.901387819 + -0.25 = -1.151387819 j = -1.151387819 Simplifying j = -1.151387819Solution
The solution to the problem is based on the solutions from the subproblems. j = {0.651387819, -1.151387819}
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