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Simplifying 5n2 + 10n + -9 = 0 Reorder the terms: -9 + 10n + 5n2 = 0 Solving -9 + 10n + 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'. -1.8 + 2n + n2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 2n + 1.8 + n2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 2n + n2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 2n + n2 = 0 + 1.8 2n + n2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 2n + n2 = 1.8 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 = 1.8 + 1 Reorder the terms: 1 + 2n + n2 = 1.8 + 1 Combine like terms: 1.8 + 1 = 2.8 1 + 2n + n2 = 2.8 Factor a perfect square on the left side: (n + 1)(n + 1) = 2.8 Calculate the square root of the right side: 1.673320053 Break this problem into two subproblems by setting (n + 1) equal to 1.673320053 and -1.673320053.Subproblem 1
n + 1 = 1.673320053 Simplifying n + 1 = 1.673320053 Reorder the terms: 1 + n = 1.673320053 Solving 1 + n = 1.673320053 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 = 1.673320053 + -1 Combine like terms: 1 + -1 = 0 0 + n = 1.673320053 + -1 n = 1.673320053 + -1 Combine like terms: 1.673320053 + -1 = 0.673320053 n = 0.673320053 Simplifying n = 0.673320053Subproblem 2
n + 1 = -1.673320053 Simplifying n + 1 = -1.673320053 Reorder the terms: 1 + n = -1.673320053 Solving 1 + n = -1.673320053 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 = -1.673320053 + -1 Combine like terms: 1 + -1 = 0 0 + n = -1.673320053 + -1 n = -1.673320053 + -1 Combine like terms: -1.673320053 + -1 = -2.673320053 n = -2.673320053 Simplifying n = -2.673320053Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.673320053, -2.673320053}
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