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Simplifying 10n2 + 10n + -17 = 0 Reorder the terms: -17 + 10n + 10n2 = 0 Solving -17 + 10n + 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 + n + n2 = 0 Move the constant term to the right: Add '1.7' to each side of the equation. -1.7 + n + 1.7 + n2 = 0 + 1.7 Reorder the terms: -1.7 + 1.7 + n + n2 = 0 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + n + n2 = 0 + 1.7 n + n2 = 0 + 1.7 Combine like terms: 0 + 1.7 = 1.7 n + n2 = 1.7 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + n2 = 1.7 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + n2 = 1.7 + 0.25 Combine like terms: 1.7 + 0.25 = 1.95 1.25 + n2 = 1.95 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 1.95 Calculate the square root of the right side: 1.396424004 Break this problem into two subproblems by setting (n + 0.5) equal to 1.396424004 and -1.396424004.Subproblem 1
n + 0.5 = 1.396424004 Simplifying n + 0.5 = 1.396424004 Reorder the terms: 0.5 + n = 1.396424004 Solving 0.5 + n = 1.396424004 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 1.396424004 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 1.396424004 + -0.5 n = 1.396424004 + -0.5 Combine like terms: 1.396424004 + -0.5 = 0.896424004 n = 0.896424004 Simplifying n = 0.896424004Subproblem 2
n + 0.5 = -1.396424004 Simplifying n + 0.5 = -1.396424004 Reorder the terms: 0.5 + n = -1.396424004 Solving 0.5 + n = -1.396424004 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -1.396424004 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -1.396424004 + -0.5 n = -1.396424004 + -0.5 Combine like terms: -1.396424004 + -0.5 = -1.896424004 n = -1.896424004 Simplifying n = -1.896424004Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.896424004, -1.896424004}
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