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Simplifying 9j2 + -3j + 2j3 = 0 Reorder the terms: -3j + 9j2 + 2j3 = 0 Solving -3j + 9j2 + 2j3 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), 'j'. j(-3 + 9j + 2j2) = 0Subproblem 1
Set the factor 'j' equal to zero and attempt to solve: Simplifying j = 0 Solving j = 0 Move all terms containing j to the left, all other terms to the right. Simplifying j = 0Subproblem 2
Set the factor '(-3 + 9j + 2j2)' equal to zero and attempt to solve: Simplifying -3 + 9j + 2j2 = 0 Solving -3 + 9j + 2j2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 4.5j + j2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 4.5j + 1.5 + j2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 4.5j + j2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 4.5j + j2 = 0 + 1.5 4.5j + j2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 4.5j + j2 = 1.5 The j term is 4.5j. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5j + 5.0625 + j2 = 1.5 + 5.0625 Reorder the terms: 5.0625 + 4.5j + j2 = 1.5 + 5.0625 Combine like terms: 1.5 + 5.0625 = 6.5625 5.0625 + 4.5j + j2 = 6.5625 Factor a perfect square on the left side: (j + 2.25)(j + 2.25) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (j + 2.25) equal to 2.561737691 and -2.561737691.Subproblem 1
j + 2.25 = 2.561737691 Simplifying j + 2.25 = 2.561737691 Reorder the terms: 2.25 + j = 2.561737691 Solving 2.25 + j = 2.561737691 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + j = 2.561737691 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + j = 2.561737691 + -2.25 j = 2.561737691 + -2.25 Combine like terms: 2.561737691 + -2.25 = 0.311737691 j = 0.311737691 Simplifying j = 0.311737691Subproblem 2
j + 2.25 = -2.561737691 Simplifying j + 2.25 = -2.561737691 Reorder the terms: 2.25 + j = -2.561737691 Solving 2.25 + j = -2.561737691 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + j = -2.561737691 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + j = -2.561737691 + -2.25 j = -2.561737691 + -2.25 Combine like terms: -2.561737691 + -2.25 = -4.811737691 j = -4.811737691 Simplifying j = -4.811737691Solution
The solution to the problem is based on the solutions from the subproblems. j = {0.311737691, -4.811737691}Solution
j = {0, 0.311737691, -4.811737691}
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