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Simplifying 150n8 + 40n4 = 15 Reorder the terms: 40n4 + 150n8 = 15 Solving 40n4 + 150n8 = 15 Solving for variable 'n'. Reorder the terms: -15 + 40n4 + 150n8 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 40n4 + 150n8 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-3 + 8n4 + 30n8) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + 8n4 + 30n8)' equal to zero and attempt to solve: Simplifying -3 + 8n4 + 30n8 = 0 Solving -3 + 8n4 + 30n8 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -0.1 + 0.2666666667n4 + n8 = 0.0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.2666666667n4 + 0.1 + n8 = 0.0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.2666666667n4 + n8 = 0.0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.2666666667n4 + n8 = 0.0 + 0.1 0.2666666667n4 + n8 = 0.0 + 0.1 Combine like terms: 0.0 + 0.1 = 0.1 0.2666666667n4 + n8 = 0.1 The n term is 0.2666666667n4. Take half its coefficient (0.1333333334). Square it (0.01777777780) and add it to both sides. Add '0.01777777780' to each side of the equation. 0.2666666667n4 + 0.01777777780 + n8 = 0.1 + 0.01777777780 Reorder the terms: 0.01777777780 + 0.2666666667n4 + n8 = 0.1 + 0.01777777780 Combine like terms: 0.1 + 0.01777777780 = 0.1177777778 0.01777777780 + 0.2666666667n4 + n8 = 0.1177777778 Factor a perfect square on the left side: (n4 + 0.1333333334)(n4 + 0.1333333334) = 0.1177777778 Calculate the square root of the right side: 0.343187671 Break this problem into two subproblems by setting (n4 + 0.1333333334) equal to 0.343187671 and -0.343187671.Subproblem 1
n4 + 0.1333333334 = 0.343187671 Simplifying n4 + 0.1333333334 = 0.343187671 Reorder the terms: 0.1333333334 + n4 = 0.343187671 Solving 0.1333333334 + n4 = 0.343187671 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.1333333334' to each side of the equation. 0.1333333334 + -0.1333333334 + n4 = 0.343187671 + -0.1333333334 Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000 0.0000000000 + n4 = 0.343187671 + -0.1333333334 n4 = 0.343187671 + -0.1333333334 Combine like terms: 0.343187671 + -0.1333333334 = 0.2098543376 n4 = 0.2098543376 Simplifying n4 = 0.2098543376 Reorder the terms: -0.2098543376 + n4 = 0.2098543376 + -0.2098543376 Combine like terms: 0.2098543376 + -0.2098543376 = 0.0000000000 -0.2098543376 + n4 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
n4 + 0.1333333334 = -0.343187671 Simplifying n4 + 0.1333333334 = -0.343187671 Reorder the terms: 0.1333333334 + n4 = -0.343187671 Solving 0.1333333334 + n4 = -0.343187671 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.1333333334' to each side of the equation. 0.1333333334 + -0.1333333334 + n4 = -0.343187671 + -0.1333333334 Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000 0.0000000000 + n4 = -0.343187671 + -0.1333333334 n4 = -0.343187671 + -0.1333333334 Combine like terms: -0.343187671 + -0.1333333334 = -0.4765210044 n4 = -0.4765210044 Simplifying n4 = -0.4765210044 Reorder the terms: 0.4765210044 + n4 = -0.4765210044 + 0.4765210044 Combine like terms: -0.4765210044 + 0.4765210044 = 0.0000000000 0.4765210044 + n4 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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