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Simplifying -7n2 = 8n + 10 Reorder the terms: -7n2 = 10 + 8n Solving -7n2 = 10 + 8n Solving for variable 'n'. Reorder the terms: -10 + -8n + -7n2 = 10 + 8n + -10 + -8n Reorder the terms: -10 + -8n + -7n2 = 10 + -10 + 8n + -8n Combine like terms: 10 + -10 = 0 -10 + -8n + -7n2 = 0 + 8n + -8n -10 + -8n + -7n2 = 8n + -8n Combine like terms: 8n + -8n = 0 -10 + -8n + -7n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 8n + 7n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 8n + 7n2)' equal to zero and attempt to solve: Simplifying 10 + 8n + 7n2 = 0 Solving 10 + 8n + 7n2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.428571429 + 1.142857143n + n2 = 0 Move the constant term to the right: Add '-1.428571429' to each side of the equation. 1.428571429 + 1.142857143n + -1.428571429 + n2 = 0 + -1.428571429 Reorder the terms: 1.428571429 + -1.428571429 + 1.142857143n + n2 = 0 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + 1.142857143n + n2 = 0 + -1.428571429 1.142857143n + n2 = 0 + -1.428571429 Combine like terms: 0 + -1.428571429 = -1.428571429 1.142857143n + n2 = -1.428571429 The n term is 1.142857143n. Take half its coefficient (0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. 1.142857143n + 0.3265306123 + n2 = -1.428571429 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143n + n2 = -1.428571429 + 0.3265306123 Combine like terms: -1.428571429 + 0.3265306123 = -1.1020408167 0.3265306123 + 1.142857143n + n2 = -1.1020408167 Factor a perfect square on the left side: (n + 0.5714285715)(n + 0.5714285715) = -1.1020408167 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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