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Simplifying -200 = 3(7n + 1) * 8n Reorder the terms: -200 = 3(1 + 7n) * 8n Reorder the terms for easier multiplication: -200 = 3 * 8n(1 + 7n) Multiply 3 * 8 -200 = 24n(1 + 7n) -200 = (1 * 24n + 7n * 24n) -200 = (24n + 168n2) Solving -200 = 24n + 168n2 Solving for variable 'n'. Reorder the terms: -200 + -24n + -168n2 = 24n + -24n + 168n2 + -168n2 Combine like terms: 24n + -24n = 0 -200 + -24n + -168n2 = 0 + 168n2 + -168n2 -200 + -24n + -168n2 = 168n2 + -168n2 Combine like terms: 168n2 + -168n2 = 0 -200 + -24n + -168n2 = 0 Factor out the Greatest Common Factor (GCF), '-8'. -8(25 + 3n + 21n2) = 0 Ignore the factor -8.Subproblem 1
Set the factor '(25 + 3n + 21n2)' equal to zero and attempt to solve: Simplifying 25 + 3n + 21n2 = 0 Solving 25 + 3n + 21n2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 1.19047619 + 0.1428571429n + n2 = 0 Move the constant term to the right: Add '-1.19047619' to each side of the equation. 1.19047619 + 0.1428571429n + -1.19047619 + n2 = 0 + -1.19047619 Reorder the terms: 1.19047619 + -1.19047619 + 0.1428571429n + n2 = 0 + -1.19047619 Combine like terms: 1.19047619 + -1.19047619 = 0.00000000 0.00000000 + 0.1428571429n + n2 = 0 + -1.19047619 0.1428571429n + n2 = 0 + -1.19047619 Combine like terms: 0 + -1.19047619 = -1.19047619 0.1428571429n + n2 = -1.19047619 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 = -1.19047619 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429n + n2 = -1.19047619 + 0.005102040819 Combine like terms: -1.19047619 + 0.005102040819 = -1.185374149181 0.005102040819 + 0.1428571429n + n2 = -1.185374149181 Factor a perfect square on the left side: (n + 0.07142857145)(n + 0.07142857145) = -1.185374149181 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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