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Simplifying 5(j + -4) * j = -8 Reorder the terms: 5(-4 + j) * j = -8 Reorder the terms for easier multiplication: 5j(-4 + j) = -8 (-4 * 5j + j * 5j) = -8 (-20j + 5j2) = -8 Solving -20j + 5j2 = -8 Solving for variable 'j'. Reorder the terms: 8 + -20j + 5j2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + -20j + 5j2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.6 + -4j + j2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -4j + -1.6 + j2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -4j + j2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -4j + j2 = 0 + -1.6 -4j + j2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -4j + j2 = -1.6 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 = -1.6 + 4 Reorder the terms: 4 + -4j + j2 = -1.6 + 4 Combine like terms: -1.6 + 4 = 2.4 4 + -4j + j2 = 2.4 Factor a perfect square on the left side: (j + -2)(j + -2) = 2.4 Calculate the square root of the right side: 1.549193338 Break this problem into two subproblems by setting (j + -2) equal to 1.549193338 and -1.549193338.Subproblem 1
j + -2 = 1.549193338 Simplifying j + -2 = 1.549193338 Reorder the terms: -2 + j = 1.549193338 Solving -2 + j = 1.549193338 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 = 1.549193338 + 2 Combine like terms: -2 + 2 = 0 0 + j = 1.549193338 + 2 j = 1.549193338 + 2 Combine like terms: 1.549193338 + 2 = 3.549193338 j = 3.549193338 Simplifying j = 3.549193338Subproblem 2
j + -2 = -1.549193338 Simplifying j + -2 = -1.549193338 Reorder the terms: -2 + j = -1.549193338 Solving -2 + j = -1.549193338 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 = -1.549193338 + 2 Combine like terms: -2 + 2 = 0 0 + j = -1.549193338 + 2 j = -1.549193338 + 2 Combine like terms: -1.549193338 + 2 = 0.450806662 j = 0.450806662 Simplifying j = 0.450806662Solution
The solution to the problem is based on the solutions from the subproblems. j = {3.549193338, 0.450806662}
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