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Simplifying 10n2 + -9n + -17 = 0 Reorder the terms: -17 + -9n + 10n2 = 0 Solving -17 + -9n + 10n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.7 + -0.9n + n2 = 0 Move the constant term to the right: Add '1.7' to each side of the equation. -1.7 + -0.9n + 1.7 + n2 = 0 + 1.7 Reorder the terms: -1.7 + 1.7 + -0.9n + n2 = 0 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + -0.9n + n2 = 0 + 1.7 -0.9n + n2 = 0 + 1.7 Combine like terms: 0 + 1.7 = 1.7 -0.9n + n2 = 1.7 The n term is -0.9n. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9n + 0.2025 + n2 = 1.7 + 0.2025 Reorder the terms: 0.2025 + -0.9n + n2 = 1.7 + 0.2025 Combine like terms: 1.7 + 0.2025 = 1.9025 0.2025 + -0.9n + n2 = 1.9025 Factor a perfect square on the left side: (n + -0.45)(n + -0.45) = 1.9025 Calculate the square root of the right side: 1.379311422 Break this problem into two subproblems by setting (n + -0.45) equal to 1.379311422 and -1.379311422.Subproblem 1
n + -0.45 = 1.379311422 Simplifying n + -0.45 = 1.379311422 Reorder the terms: -0.45 + n = 1.379311422 Solving -0.45 + n = 1.379311422 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + n = 1.379311422 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + n = 1.379311422 + 0.45 n = 1.379311422 + 0.45 Combine like terms: 1.379311422 + 0.45 = 1.829311422 n = 1.829311422 Simplifying n = 1.829311422Subproblem 2
n + -0.45 = -1.379311422 Simplifying n + -0.45 = -1.379311422 Reorder the terms: -0.45 + n = -1.379311422 Solving -0.45 + n = -1.379311422 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + n = -1.379311422 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + n = -1.379311422 + 0.45 n = -1.379311422 + 0.45 Combine like terms: -1.379311422 + 0.45 = -0.929311422 n = -0.929311422 Simplifying n = -0.929311422Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.829311422, -0.929311422}
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