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Simplifying -5n2 + 11n + 40 = 0 Reorder the terms: 40 + 11n + -5n2 = 0 Solving 40 + 11n + -5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -8 + -2.2n + n2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -2.2n + 8 + n2 = 0 + 8 Reorder the terms: -8 + 8 + -2.2n + n2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -2.2n + n2 = 0 + 8 -2.2n + n2 = 0 + 8 Combine like terms: 0 + 8 = 8 -2.2n + n2 = 8 The n term is -2.2n. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2n + 1.21 + n2 = 8 + 1.21 Reorder the terms: 1.21 + -2.2n + n2 = 8 + 1.21 Combine like terms: 8 + 1.21 = 9.21 1.21 + -2.2n + n2 = 9.21 Factor a perfect square on the left side: (n + -1.1)(n + -1.1) = 9.21 Calculate the square root of the right side: 3.034798181 Break this problem into two subproblems by setting (n + -1.1) equal to 3.034798181 and -3.034798181.Subproblem 1
n + -1.1 = 3.034798181 Simplifying n + -1.1 = 3.034798181 Reorder the terms: -1.1 + n = 3.034798181 Solving -1.1 + n = 3.034798181 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + n = 3.034798181 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + n = 3.034798181 + 1.1 n = 3.034798181 + 1.1 Combine like terms: 3.034798181 + 1.1 = 4.134798181 n = 4.134798181 Simplifying n = 4.134798181Subproblem 2
n + -1.1 = -3.034798181 Simplifying n + -1.1 = -3.034798181 Reorder the terms: -1.1 + n = -3.034798181 Solving -1.1 + n = -3.034798181 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + n = -3.034798181 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + n = -3.034798181 + 1.1 n = -3.034798181 + 1.1 Combine like terms: -3.034798181 + 1.1 = -1.934798181 n = -1.934798181 Simplifying n = -1.934798181Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.134798181, -1.934798181}
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