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Simplifying 4n2 + n + -37 = 0 Reorder the terms: -37 + n + 4n2 = 0 Solving -37 + n + 4n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9.25 + 0.25n + n2 = 0 Move the constant term to the right: Add '9.25' to each side of the equation. -9.25 + 0.25n + 9.25 + n2 = 0 + 9.25 Reorder the terms: -9.25 + 9.25 + 0.25n + n2 = 0 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + 0.25n + n2 = 0 + 9.25 0.25n + n2 = 0 + 9.25 Combine like terms: 0 + 9.25 = 9.25 0.25n + n2 = 9.25 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. 0.25n + 0.25 + n2 = 9.25 + 0.25 Reorder the terms: 0.25 + 0.25n + n2 = 9.25 + 0.25 Combine like terms: 9.25 + 0.25 = 9.5 0.25 + 0.25n + n2 = 9.5 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (n + 0.5) equal to 3.082207001 and -3.082207001.Subproblem 1
n + 0.5 = 3.082207001 Simplifying n + 0.5 = 3.082207001 Reorder the terms: 0.5 + n = 3.082207001 Solving 0.5 + n = 3.082207001 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 = 3.082207001 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 3.082207001 + -0.5 n = 3.082207001 + -0.5 Combine like terms: 3.082207001 + -0.5 = 2.582207001 n = 2.582207001 Simplifying n = 2.582207001Subproblem 2
n + 0.5 = -3.082207001 Simplifying n + 0.5 = -3.082207001 Reorder the terms: 0.5 + n = -3.082207001 Solving 0.5 + n = -3.082207001 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 = -3.082207001 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -3.082207001 + -0.5 n = -3.082207001 + -0.5 Combine like terms: -3.082207001 + -0.5 = -3.582207001 n = -3.582207001 Simplifying n = -3.582207001Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.582207001, -3.582207001}
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