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Simplifying 4n2 + n + -1900 = 0 Reorder the terms: -1900 + n + 4n2 = 0 Solving -1900 + 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'. -475 + 0.25n + n2 = 0 Move the constant term to the right: Add '475' to each side of the equation. -475 + 0.25n + 475 + n2 = 0 + 475 Reorder the terms: -475 + 475 + 0.25n + n2 = 0 + 475 Combine like terms: -475 + 475 = 0 0 + 0.25n + n2 = 0 + 475 0.25n + n2 = 0 + 475 Combine like terms: 0 + 475 = 475 0.25n + n2 = 475 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 = 475 + 0.25 Reorder the terms: 0.25 + 0.25n + n2 = 475 + 0.25 Combine like terms: 475 + 0.25 = 475.25 0.25 + 0.25n + n2 = 475.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 475.25 Calculate the square root of the right side: 21.800229357 Break this problem into two subproblems by setting (n + 0.5) equal to 21.800229357 and -21.800229357.Subproblem 1
n + 0.5 = 21.800229357 Simplifying n + 0.5 = 21.800229357 Reorder the terms: 0.5 + n = 21.800229357 Solving 0.5 + n = 21.800229357 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 = 21.800229357 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 21.800229357 + -0.5 n = 21.800229357 + -0.5 Combine like terms: 21.800229357 + -0.5 = 21.300229357 n = 21.300229357 Simplifying n = 21.300229357Subproblem 2
n + 0.5 = -21.800229357 Simplifying n + 0.5 = -21.800229357 Reorder the terms: 0.5 + n = -21.800229357 Solving 0.5 + n = -21.800229357 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 = -21.800229357 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -21.800229357 + -0.5 n = -21.800229357 + -0.5 Combine like terms: -21.800229357 + -0.5 = -22.300229357 n = -22.300229357 Simplifying n = -22.300229357Solution
The solution to the problem is based on the solutions from the subproblems. n = {21.300229357, -22.300229357}
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