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Simplifying (j + -3) * j + 4 + j = 196 Reorder the terms: (-3 + j) * j + 4 + j = 196 Reorder the terms for easier multiplication: j(-3 + j) + 4 + j = 196 (-3 * j + j * j) + 4 + j = 196 (-3j + j2) + 4 + j = 196 Reorder the terms: 4 + -3j + j + j2 = 196 Combine like terms: -3j + j = -2j 4 + -2j + j2 = 196 Solving 4 + -2j + j2 = 196 Solving for variable 'j'. Reorder the terms: 4 + -196 + -2j + j2 = 196 + -196 Combine like terms: 4 + -196 = -192 -192 + -2j + j2 = 196 + -196 Combine like terms: 196 + -196 = 0 -192 + -2j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '192' to each side of the equation. -192 + -2j + 192 + j2 = 0 + 192 Reorder the terms: -192 + 192 + -2j + j2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + -2j + j2 = 0 + 192 -2j + j2 = 0 + 192 Combine like terms: 0 + 192 = 192 -2j + j2 = 192 The j term is -2j. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2j + 1 + j2 = 192 + 1 Reorder the terms: 1 + -2j + j2 = 192 + 1 Combine like terms: 192 + 1 = 193 1 + -2j + j2 = 193 Factor a perfect square on the left side: (j + -1)(j + -1) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (j + -1) equal to 13.892443989 and -13.892443989.Subproblem 1
j + -1 = 13.892443989 Simplifying j + -1 = 13.892443989 Reorder the terms: -1 + j = 13.892443989 Solving -1 + j = 13.892443989 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + j = 13.892443989 + 1 Combine like terms: -1 + 1 = 0 0 + j = 13.892443989 + 1 j = 13.892443989 + 1 Combine like terms: 13.892443989 + 1 = 14.892443989 j = 14.892443989 Simplifying j = 14.892443989Subproblem 2
j + -1 = -13.892443989 Simplifying j + -1 = -13.892443989 Reorder the terms: -1 + j = -13.892443989 Solving -1 + j = -13.892443989 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + j = -13.892443989 + 1 Combine like terms: -1 + 1 = 0 0 + j = -13.892443989 + 1 j = -13.892443989 + 1 Combine like terms: -13.892443989 + 1 = -12.892443989 j = -12.892443989 Simplifying j = -12.892443989Solution
The solution to the problem is based on the solutions from the subproblems. j = {14.892443989, -12.892443989}
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