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Simplifying -7j2 + 5j + 3 = 0 Reorder the terms: 3 + 5j + -7j2 = 0 Solving 3 + 5j + -7j2 = 0 Solving for variable 'j'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.4285714286 + -0.7142857143j + j2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -0.7142857143j + 0.4285714286 + j2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -0.7142857143j + j2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -0.7142857143j + j2 = 0 + 0.4285714286 -0.7142857143j + j2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -0.7142857143j + j2 = 0.4285714286 The j term is -0.7142857143j. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143j + 0.1275510204 + j2 = 0.4285714286 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143j + j2 = 0.4285714286 + 0.1275510204 Combine like terms: 0.4285714286 + 0.1275510204 = 0.556122449 0.1275510204 + -0.7142857143j + j2 = 0.556122449 Factor a perfect square on the left side: (j + -0.3571428572)(j + -0.3571428572) = 0.556122449 Calculate the square root of the right side: 0.745736179 Break this problem into two subproblems by setting (j + -0.3571428572) equal to 0.745736179 and -0.745736179.Subproblem 1
j + -0.3571428572 = 0.745736179 Simplifying j + -0.3571428572 = 0.745736179 Reorder the terms: -0.3571428572 + j = 0.745736179 Solving -0.3571428572 + j = 0.745736179 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + j = 0.745736179 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + j = 0.745736179 + 0.3571428572 j = 0.745736179 + 0.3571428572 Combine like terms: 0.745736179 + 0.3571428572 = 1.1028790362 j = 1.1028790362 Simplifying j = 1.1028790362Subproblem 2
j + -0.3571428572 = -0.745736179 Simplifying j + -0.3571428572 = -0.745736179 Reorder the terms: -0.3571428572 + j = -0.745736179 Solving -0.3571428572 + j = -0.745736179 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + j = -0.745736179 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + j = -0.745736179 + 0.3571428572 j = -0.745736179 + 0.3571428572 Combine like terms: -0.745736179 + 0.3571428572 = -0.3885933218 j = -0.3885933218 Simplifying j = -0.3885933218Solution
The solution to the problem is based on the solutions from the subproblems. j = {1.1028790362, -0.3885933218}
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