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Simplifying 27j2 + -6j + -48 = 0 Reorder the terms: -48 + -6j + 27j2 = 0 Solving -48 + -6j + 27j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '3'. 3(-16 + -2j + 9j2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-16 + -2j + 9j2)' equal to zero and attempt to solve: Simplifying -16 + -2j + 9j2 = 0 Solving -16 + -2j + 9j2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.777777778 + -0.2222222222j + j2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -0.2222222222j + 1.777777778 + j2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -0.2222222222j + j2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -0.2222222222j + j2 = 0 + 1.777777778 -0.2222222222j + j2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -0.2222222222j + j2 = 1.777777778 The j term is -0.2222222222j. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222j + 0.01234567901 + j2 = 1.777777778 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222j + j2 = 1.777777778 + 0.01234567901 Combine like terms: 1.777777778 + 0.01234567901 = 1.79012345701 0.01234567901 + -0.2222222222j + j2 = 1.79012345701 Factor a perfect square on the left side: (j + -0.1111111111)(j + -0.1111111111) = 1.79012345701 Calculate the square root of the right side: 1.337954953 Break this problem into two subproblems by setting (j + -0.1111111111) equal to 1.337954953 and -1.337954953.Subproblem 1
j + -0.1111111111 = 1.337954953 Simplifying j + -0.1111111111 = 1.337954953 Reorder the terms: -0.1111111111 + j = 1.337954953 Solving -0.1111111111 + j = 1.337954953 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + j = 1.337954953 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + j = 1.337954953 + 0.1111111111 j = 1.337954953 + 0.1111111111 Combine like terms: 1.337954953 + 0.1111111111 = 1.4490660641 j = 1.4490660641 Simplifying j = 1.4490660641Subproblem 2
j + -0.1111111111 = -1.337954953 Simplifying j + -0.1111111111 = -1.337954953 Reorder the terms: -0.1111111111 + j = -1.337954953 Solving -0.1111111111 + j = -1.337954953 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + j = -1.337954953 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + j = -1.337954953 + 0.1111111111 j = -1.337954953 + 0.1111111111 Combine like terms: -1.337954953 + 0.1111111111 = -1.2268438419 j = -1.2268438419 Simplifying j = -1.2268438419Solution
The solution to the problem is based on the solutions from the subproblems. j = {1.4490660641, -1.2268438419}Solution
j = {1.4490660641, -1.2268438419}
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