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Simplifying -3j2 + 12j + 21 = 0 Reorder the terms: 21 + 12j + -3j2 = 0 Solving 21 + 12j + -3j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '3'. 3(7 + 4j + -1j2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + 4j + -1j2)' equal to zero and attempt to solve: Simplifying 7 + 4j + -1j2 = 0 Solving 7 + 4j + -1j2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -4j + j2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -4j + 7 + j2 = 0 + 7 Reorder the terms: -7 + 7 + -4j + j2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4j + j2 = 0 + 7 -4j + j2 = 0 + 7 Combine like terms: 0 + 7 = 7 -4j + j2 = 7 The j term is -4j. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4j + 4 + j2 = 7 + 4 Reorder the terms: 4 + -4j + j2 = 7 + 4 Combine like terms: 7 + 4 = 11 4 + -4j + j2 = 11 Factor a perfect square on the left side: (j + -2)(j + -2) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (j + -2) equal to 3.31662479 and -3.31662479.Subproblem 1
j + -2 = 3.31662479 Simplifying j + -2 = 3.31662479 Reorder the terms: -2 + j = 3.31662479 Solving -2 + j = 3.31662479 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + j = 3.31662479 + 2 Combine like terms: -2 + 2 = 0 0 + j = 3.31662479 + 2 j = 3.31662479 + 2 Combine like terms: 3.31662479 + 2 = 5.31662479 j = 5.31662479 Simplifying j = 5.31662479Subproblem 2
j + -2 = -3.31662479 Simplifying j + -2 = -3.31662479 Reorder the terms: -2 + j = -3.31662479 Solving -2 + j = -3.31662479 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + j = -3.31662479 + 2 Combine like terms: -2 + 2 = 0 0 + j = -3.31662479 + 2 j = -3.31662479 + 2 Combine like terms: -3.31662479 + 2 = -1.31662479 j = -1.31662479 Simplifying j = -1.31662479Solution
The solution to the problem is based on the solutions from the subproblems. j = {5.31662479, -1.31662479}Solution
j = {5.31662479, -1.31662479}
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