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Simplifying -2j2 + -16j + 94 = 0 Reorder the terms: 94 + -16j + -2j2 = 0 Solving 94 + -16j + -2j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '2'. 2(47 + -8j + -1j2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(47 + -8j + -1j2)' equal to zero and attempt to solve: Simplifying 47 + -8j + -1j2 = 0 Solving 47 + -8j + -1j2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -47 + 8j + j2 = 0 Move the constant term to the right: Add '47' to each side of the equation. -47 + 8j + 47 + j2 = 0 + 47 Reorder the terms: -47 + 47 + 8j + j2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 8j + j2 = 0 + 47 8j + j2 = 0 + 47 Combine like terms: 0 + 47 = 47 8j + j2 = 47 The j term is 8j. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8j + 16 + j2 = 47 + 16 Reorder the terms: 16 + 8j + j2 = 47 + 16 Combine like terms: 47 + 16 = 63 16 + 8j + j2 = 63 Factor a perfect square on the left side: (j + 4)(j + 4) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (j + 4) equal to 7.937253933 and -7.937253933.Subproblem 1
j + 4 = 7.937253933 Simplifying j + 4 = 7.937253933 Reorder the terms: 4 + j = 7.937253933 Solving 4 + j = 7.937253933 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + j = 7.937253933 + -4 Combine like terms: 4 + -4 = 0 0 + j = 7.937253933 + -4 j = 7.937253933 + -4 Combine like terms: 7.937253933 + -4 = 3.937253933 j = 3.937253933 Simplifying j = 3.937253933Subproblem 2
j + 4 = -7.937253933 Simplifying j + 4 = -7.937253933 Reorder the terms: 4 + j = -7.937253933 Solving 4 + j = -7.937253933 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + j = -7.937253933 + -4 Combine like terms: 4 + -4 = 0 0 + j = -7.937253933 + -4 j = -7.937253933 + -4 Combine like terms: -7.937253933 + -4 = -11.937253933 j = -11.937253933 Simplifying j = -11.937253933Solution
The solution to the problem is based on the solutions from the subproblems. j = {3.937253933, -11.937253933}Solution
j = {3.937253933, -11.937253933}
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