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Simplifying 16n2 + 8n + -25 = 0 Reorder the terms: -25 + 8n + 16n2 = 0 Solving -25 + 8n + 16n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.5625 + 0.5n + n2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + 0.5n + 1.5625 + n2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + 0.5n + n2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + 0.5n + n2 = 0 + 1.5625 0.5n + n2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 0.5n + n2 = 1.5625 The n term is 0.5n. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5n + 0.0625 + n2 = 1.5625 + 0.0625 Reorder the terms: 0.0625 + 0.5n + n2 = 1.5625 + 0.0625 Combine like terms: 1.5625 + 0.0625 = 1.625 0.0625 + 0.5n + n2 = 1.625 Factor a perfect square on the left side: (n + 0.25)(n + 0.25) = 1.625 Calculate the square root of the right side: 1.274754878 Break this problem into two subproblems by setting (n + 0.25) equal to 1.274754878 and -1.274754878.Subproblem 1
n + 0.25 = 1.274754878 Simplifying n + 0.25 = 1.274754878 Reorder the terms: 0.25 + n = 1.274754878 Solving 0.25 + n = 1.274754878 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + n = 1.274754878 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + n = 1.274754878 + -0.25 n = 1.274754878 + -0.25 Combine like terms: 1.274754878 + -0.25 = 1.024754878 n = 1.024754878 Simplifying n = 1.024754878Subproblem 2
n + 0.25 = -1.274754878 Simplifying n + 0.25 = -1.274754878 Reorder the terms: 0.25 + n = -1.274754878 Solving 0.25 + n = -1.274754878 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + n = -1.274754878 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + n = -1.274754878 + -0.25 n = -1.274754878 + -0.25 Combine like terms: -1.274754878 + -0.25 = -1.524754878 n = -1.524754878 Simplifying n = -1.524754878Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.024754878, -1.524754878}
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