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Simplifying 7j2 + -4j + -9 = 0 Reorder the terms: -9 + -4j + 7j2 = 0 Solving -9 + -4j + 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'. -1.285714286 + -0.5714285714j + j2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + -0.5714285714j + 1.285714286 + j2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + -0.5714285714j + j2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + -0.5714285714j + j2 = 0 + 1.285714286 -0.5714285714j + j2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 -0.5714285714j + j2 = 1.285714286 The j term is -0.5714285714j. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714j + 0.08163265305 + j2 = 1.285714286 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714j + j2 = 1.285714286 + 0.08163265305 Combine like terms: 1.285714286 + 0.08163265305 = 1.36734693905 0.08163265305 + -0.5714285714j + j2 = 1.36734693905 Factor a perfect square on the left side: (j + -0.2857142857)(j + -0.2857142857) = 1.36734693905 Calculate the square root of the right side: 1.16933611 Break this problem into two subproblems by setting (j + -0.2857142857) equal to 1.16933611 and -1.16933611.Subproblem 1
j + -0.2857142857 = 1.16933611 Simplifying j + -0.2857142857 = 1.16933611 Reorder the terms: -0.2857142857 + j = 1.16933611 Solving -0.2857142857 + j = 1.16933611 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + j = 1.16933611 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + j = 1.16933611 + 0.2857142857 j = 1.16933611 + 0.2857142857 Combine like terms: 1.16933611 + 0.2857142857 = 1.4550503957 j = 1.4550503957 Simplifying j = 1.4550503957Subproblem 2
j + -0.2857142857 = -1.16933611 Simplifying j + -0.2857142857 = -1.16933611 Reorder the terms: -0.2857142857 + j = -1.16933611 Solving -0.2857142857 + j = -1.16933611 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + j = -1.16933611 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + j = -1.16933611 + 0.2857142857 j = -1.16933611 + 0.2857142857 Combine like terms: -1.16933611 + 0.2857142857 = -0.8836218243 j = -0.8836218243 Simplifying j = -0.8836218243Solution
The solution to the problem is based on the solutions from the subproblems. j = {1.4550503957, -0.8836218243}
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