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Simplifying -5n(-8)(1 + 7n) = -8 Reorder the terms for easier multiplication: -5 * -8n(1 + 7n) = -8 Multiply -5 * -8 40n(1 + 7n) = -8 (1 * 40n + 7n * 40n) = -8 (40n + 280n2) = -8 Solving 40n + 280n2 = -8 Solving for variable 'n'. Reorder the terms: 8 + 40n + 280n2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + 40n + 280n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(1 + 5n + 35n2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(1 + 5n + 35n2)' equal to zero and attempt to solve: Simplifying 1 + 5n + 35n2 = 0 Solving 1 + 5n + 35n2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. 0.02857142857 + 0.1428571429n + n2 = 0 Move the constant term to the right: Add '-0.02857142857' to each side of the equation. 0.02857142857 + 0.1428571429n + -0.02857142857 + n2 = 0 + -0.02857142857 Reorder the terms: 0.02857142857 + -0.02857142857 + 0.1428571429n + n2 = 0 + -0.02857142857 Combine like terms: 0.02857142857 + -0.02857142857 = 0.00000000000 0.00000000000 + 0.1428571429n + n2 = 0 + -0.02857142857 0.1428571429n + n2 = 0 + -0.02857142857 Combine like terms: 0 + -0.02857142857 = -0.02857142857 0.1428571429n + n2 = -0.02857142857 The n term is 0.1428571429n. Take half its coefficient (0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. 0.1428571429n + 0.005102040819 + n2 = -0.02857142857 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429n + n2 = -0.02857142857 + 0.005102040819 Combine like terms: -0.02857142857 + 0.005102040819 = -0.023469387751 0.005102040819 + 0.1428571429n + n2 = -0.023469387751 Factor a perfect square on the left side: (n + 0.07142857145)(n + 0.07142857145) = -0.023469387751 Can't calculate square root of the right side. 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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