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Simplifying -3(j + 3) * 9j = -15 Reorder the terms: -3(3 + j) * 9j = -15 Reorder the terms for easier multiplication: -3 * 9j(3 + j) = -15 Multiply -3 * 9 -27j(3 + j) = -15 (3 * -27j + j * -27j) = -15 (-81j + -27j2) = -15 Solving -81j + -27j2 = -15 Solving for variable 'j'. Reorder the terms: 15 + -81j + -27j2 = -15 + 15 Combine like terms: -15 + 15 = 0 15 + -81j + -27j2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(5 + -27j + -9j2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -27j + -9j2)' equal to zero and attempt to solve: Simplifying 5 + -27j + -9j2 = 0 Solving 5 + -27j + -9j2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.5555555556 + 3j + j2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 3j + 0.5555555556 + j2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 3j + j2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 3j + j2 = 0 + 0.5555555556 3j + j2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 3j + j2 = 0.5555555556 The j term is 3j. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3j + 2.25 + j2 = 0.5555555556 + 2.25 Reorder the terms: 2.25 + 3j + j2 = 0.5555555556 + 2.25 Combine like terms: 0.5555555556 + 2.25 = 2.8055555556 2.25 + 3j + j2 = 2.8055555556 Factor a perfect square on the left side: (j + 1.5)(j + 1.5) = 2.8055555556 Calculate the square root of the right side: 1.67497927 Break this problem into two subproblems by setting (j + 1.5) equal to 1.67497927 and -1.67497927.Subproblem 1
j + 1.5 = 1.67497927 Simplifying j + 1.5 = 1.67497927 Reorder the terms: 1.5 + j = 1.67497927 Solving 1.5 + j = 1.67497927 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + j = 1.67497927 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + j = 1.67497927 + -1.5 j = 1.67497927 + -1.5 Combine like terms: 1.67497927 + -1.5 = 0.17497927 j = 0.17497927 Simplifying j = 0.17497927Subproblem 2
j + 1.5 = -1.67497927 Simplifying j + 1.5 = -1.67497927 Reorder the terms: 1.5 + j = -1.67497927 Solving 1.5 + j = -1.67497927 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + j = -1.67497927 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + j = -1.67497927 + -1.5 j = -1.67497927 + -1.5 Combine like terms: -1.67497927 + -1.5 = -3.17497927 j = -3.17497927 Simplifying j = -3.17497927Solution
The solution to the problem is based on the solutions from the subproblems. j = {0.17497927, -3.17497927}Solution
j = {0.17497927, -3.17497927}
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