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Simplifying 10n2 + 20n + -72 = 0 Reorder the terms: -72 + 20n + 10n2 = 0 Solving -72 + 20n + 10n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-36 + 10n + 5n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-36 + 10n + 5n2)' equal to zero and attempt to solve: Simplifying -36 + 10n + 5n2 = 0 Solving -36 + 10n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.2 + 2n + n2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + 2n + 7.2 + n2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + 2n + n2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + 2n + n2 = 0 + 7.2 2n + n2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 2n + n2 = 7.2 The n term is 2n. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2n + 1 + n2 = 7.2 + 1 Reorder the terms: 1 + 2n + n2 = 7.2 + 1 Combine like terms: 7.2 + 1 = 8.2 1 + 2n + n2 = 8.2 Factor a perfect square on the left side: (n + 1)(n + 1) = 8.2 Calculate the square root of the right side: 2.863564213 Break this problem into two subproblems by setting (n + 1) equal to 2.863564213 and -2.863564213.Subproblem 1
n + 1 = 2.863564213 Simplifying n + 1 = 2.863564213 Reorder the terms: 1 + n = 2.863564213 Solving 1 + n = 2.863564213 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 2.863564213 + -1 Combine like terms: 1 + -1 = 0 0 + n = 2.863564213 + -1 n = 2.863564213 + -1 Combine like terms: 2.863564213 + -1 = 1.863564213 n = 1.863564213 Simplifying n = 1.863564213Subproblem 2
n + 1 = -2.863564213 Simplifying n + 1 = -2.863564213 Reorder the terms: 1 + n = -2.863564213 Solving 1 + n = -2.863564213 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = -2.863564213 + -1 Combine like terms: 1 + -1 = 0 0 + n = -2.863564213 + -1 n = -2.863564213 + -1 Combine like terms: -2.863564213 + -1 = -3.863564213 n = -3.863564213 Simplifying n = -3.863564213Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.863564213, -3.863564213}Solution
n = {1.863564213, -3.863564213}
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