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Simplifying -10n2 + -26n + 3636 = 0 Reorder the terms: 3636 + -26n + -10n2 = 0 Solving 3636 + -26n + -10n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(1818 + -13n + -5n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1818 + -13n + -5n2)' equal to zero and attempt to solve: Simplifying 1818 + -13n + -5n2 = 0 Solving 1818 + -13n + -5n2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -363.6 + 2.6n + n2 = 0 Move the constant term to the right: Add '363.6' to each side of the equation. -363.6 + 2.6n + 363.6 + n2 = 0 + 363.6 Reorder the terms: -363.6 + 363.6 + 2.6n + n2 = 0 + 363.6 Combine like terms: -363.6 + 363.6 = 0.0 0.0 + 2.6n + n2 = 0 + 363.6 2.6n + n2 = 0 + 363.6 Combine like terms: 0 + 363.6 = 363.6 2.6n + n2 = 363.6 The n term is 2.6n. Take half its coefficient (1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. 2.6n + 1.69 + n2 = 363.6 + 1.69 Reorder the terms: 1.69 + 2.6n + n2 = 363.6 + 1.69 Combine like terms: 363.6 + 1.69 = 365.29 1.69 + 2.6n + n2 = 365.29 Factor a perfect square on the left side: (n + 1.3)(n + 1.3) = 365.29 Calculate the square root of the right side: 19.112561314 Break this problem into two subproblems by setting (n + 1.3) equal to 19.112561314 and -19.112561314.Subproblem 1
n + 1.3 = 19.112561314 Simplifying n + 1.3 = 19.112561314 Reorder the terms: 1.3 + n = 19.112561314 Solving 1.3 + n = 19.112561314 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + n = 19.112561314 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + n = 19.112561314 + -1.3 n = 19.112561314 + -1.3 Combine like terms: 19.112561314 + -1.3 = 17.812561314 n = 17.812561314 Simplifying n = 17.812561314Subproblem 2
n + 1.3 = -19.112561314 Simplifying n + 1.3 = -19.112561314 Reorder the terms: 1.3 + n = -19.112561314 Solving 1.3 + n = -19.112561314 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + n = -19.112561314 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + n = -19.112561314 + -1.3 n = -19.112561314 + -1.3 Combine like terms: -19.112561314 + -1.3 = -20.412561314 n = -20.412561314 Simplifying n = -20.412561314Solution
The solution to the problem is based on the solutions from the subproblems. n = {17.812561314, -20.412561314}Solution
n = {17.812561314, -20.412561314}
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