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Simplifying 2j2 + 26j = 20 Reorder the terms: 26j + 2j2 = 20 Solving 26j + 2j2 = 20 Solving for variable 'j'. Reorder the terms: -20 + 26j + 2j2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 26j + 2j2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 13j + j2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + 13j + j2)' equal to zero and attempt to solve: Simplifying -10 + 13j + j2 = 0 Solving -10 + 13j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 13j + 10 + j2 = 0 + 10 Reorder the terms: -10 + 10 + 13j + j2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 13j + j2 = 0 + 10 13j + j2 = 0 + 10 Combine like terms: 0 + 10 = 10 13j + j2 = 10 The j term is 13j. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13j + 42.25 + j2 = 10 + 42.25 Reorder the terms: 42.25 + 13j + j2 = 10 + 42.25 Combine like terms: 10 + 42.25 = 52.25 42.25 + 13j + j2 = 52.25 Factor a perfect square on the left side: (j + 6.5)(j + 6.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (j + 6.5) equal to 7.228416147 and -7.228416147.Subproblem 1
j + 6.5 = 7.228416147 Simplifying j + 6.5 = 7.228416147 Reorder the terms: 6.5 + j = 7.228416147 Solving 6.5 + j = 7.228416147 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + j = 7.228416147 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + j = 7.228416147 + -6.5 j = 7.228416147 + -6.5 Combine like terms: 7.228416147 + -6.5 = 0.728416147 j = 0.728416147 Simplifying j = 0.728416147Subproblem 2
j + 6.5 = -7.228416147 Simplifying j + 6.5 = -7.228416147 Reorder the terms: 6.5 + j = -7.228416147 Solving 6.5 + j = -7.228416147 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + j = -7.228416147 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + j = -7.228416147 + -6.5 j = -7.228416147 + -6.5 Combine like terms: -7.228416147 + -6.5 = -13.728416147 j = -13.728416147 Simplifying j = -13.728416147Solution
The solution to the problem is based on the solutions from the subproblems. j = {0.728416147, -13.728416147}Solution
j = {0.728416147, -13.728416147}
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