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Simplifying 25n2 + 40n + -16 = 0 Reorder the terms: -16 + 40n + 25n2 = 0 Solving -16 + 40n + 25n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.64 + 1.6n + n2 = 0 Move the constant term to the right: Add '0.64' to each side of the equation. -0.64 + 1.6n + 0.64 + n2 = 0 + 0.64 Reorder the terms: -0.64 + 0.64 + 1.6n + n2 = 0 + 0.64 Combine like terms: -0.64 + 0.64 = 0.00 0.00 + 1.6n + n2 = 0 + 0.64 1.6n + n2 = 0 + 0.64 Combine like terms: 0 + 0.64 = 0.64 1.6n + n2 = 0.64 The n term is 1.6n. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6n + 0.64 + n2 = 0.64 + 0.64 Reorder the terms: 0.64 + 1.6n + n2 = 0.64 + 0.64 Combine like terms: 0.64 + 0.64 = 1.28 0.64 + 1.6n + n2 = 1.28 Factor a perfect square on the left side: (n + 0.8)(n + 0.8) = 1.28 Calculate the square root of the right side: 1.13137085 Break this problem into two subproblems by setting (n + 0.8) equal to 1.13137085 and -1.13137085.Subproblem 1
n + 0.8 = 1.13137085 Simplifying n + 0.8 = 1.13137085 Reorder the terms: 0.8 + n = 1.13137085 Solving 0.8 + n = 1.13137085 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + n = 1.13137085 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + n = 1.13137085 + -0.8 n = 1.13137085 + -0.8 Combine like terms: 1.13137085 + -0.8 = 0.33137085 n = 0.33137085 Simplifying n = 0.33137085Subproblem 2
n + 0.8 = -1.13137085 Simplifying n + 0.8 = -1.13137085 Reorder the terms: 0.8 + n = -1.13137085 Solving 0.8 + n = -1.13137085 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + n = -1.13137085 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + n = -1.13137085 + -0.8 n = -1.13137085 + -0.8 Combine like terms: -1.13137085 + -0.8 = -1.93137085 n = -1.93137085 Simplifying n = -1.93137085Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.33137085, -1.93137085}
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