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Simplifying -4j2 + -56j = 100 Reorder the terms: -56j + -4j2 = 100 Solving -56j + -4j2 = 100 Solving for variable 'j'. Reorder the terms: -100 + -56j + -4j2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + -56j + -4j2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(25 + 14j + j2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(25 + 14j + j2)' equal to zero and attempt to solve: Simplifying 25 + 14j + j2 = 0 Solving 25 + 14j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 14j + -25 + j2 = 0 + -25 Reorder the terms: 25 + -25 + 14j + j2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 14j + j2 = 0 + -25 14j + j2 = 0 + -25 Combine like terms: 0 + -25 = -25 14j + j2 = -25 The j term is 14j. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14j + 49 + j2 = -25 + 49 Reorder the terms: 49 + 14j + j2 = -25 + 49 Combine like terms: -25 + 49 = 24 49 + 14j + j2 = 24 Factor a perfect square on the left side: (j + 7)(j + 7) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (j + 7) equal to 4.898979486 and -4.898979486.Subproblem 1
j + 7 = 4.898979486 Simplifying j + 7 = 4.898979486 Reorder the terms: 7 + j = 4.898979486 Solving 7 + j = 4.898979486 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + j = 4.898979486 + -7 Combine like terms: 7 + -7 = 0 0 + j = 4.898979486 + -7 j = 4.898979486 + -7 Combine like terms: 4.898979486 + -7 = -2.101020514 j = -2.101020514 Simplifying j = -2.101020514Subproblem 2
j + 7 = -4.898979486 Simplifying j + 7 = -4.898979486 Reorder the terms: 7 + j = -4.898979486 Solving 7 + j = -4.898979486 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + j = -4.898979486 + -7 Combine like terms: 7 + -7 = 0 0 + j = -4.898979486 + -7 j = -4.898979486 + -7 Combine like terms: -4.898979486 + -7 = -11.898979486 j = -11.898979486 Simplifying j = -11.898979486Solution
The solution to the problem is based on the solutions from the subproblems. j = {-2.101020514, -11.898979486}Solution
j = {-2.101020514, -11.898979486}
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