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Simplifying 0 = n2 + n + -1600 Reorder the terms: 0 = -1600 + n + n2 Solving 0 = -1600 + n + n2 Solving for variable 'n'. Combine like terms: 0 + 1600 = 1600 1600 + -1n + -1n2 = -1600 + n + n2 + 1600 + -1n + -1n2 Reorder the terms: 1600 + -1n + -1n2 = -1600 + 1600 + n + -1n + n2 + -1n2 Combine like terms: -1600 + 1600 = 0 1600 + -1n + -1n2 = 0 + n + -1n + n2 + -1n2 1600 + -1n + -1n2 = n + -1n + n2 + -1n2 Combine like terms: n + -1n = 0 1600 + -1n + -1n2 = 0 + n2 + -1n2 1600 + -1n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 1600 + -1n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1600 + n + n2 = 0 Move the constant term to the right: Add '1600' to each side of the equation. -1600 + n + 1600 + n2 = 0 + 1600 Reorder the terms: -1600 + 1600 + n + n2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + n + n2 = 0 + 1600 n + n2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 n + n2 = 1600 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 = 1600 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + n2 = 1600 + 0.25 Combine like terms: 1600 + 0.25 = 1600.25 1.25 + n2 = 1600.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 1600.25 Calculate the square root of the right side: 40.003124878 Break this problem into two subproblems by setting (n + 0.5) equal to 40.003124878 and -40.003124878.Subproblem 1
n + 0.5 = 40.003124878 Simplifying n + 0.5 = 40.003124878 Reorder the terms: 0.5 + n = 40.003124878 Solving 0.5 + n = 40.003124878 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 = 40.003124878 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 40.003124878 + -0.5 n = 40.003124878 + -0.5 Combine like terms: 40.003124878 + -0.5 = 39.503124878 n = 39.503124878 Simplifying n = 39.503124878Subproblem 2
n + 0.5 = -40.003124878 Simplifying n + 0.5 = -40.003124878 Reorder the terms: 0.5 + n = -40.003124878 Solving 0.5 + n = -40.003124878 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 = -40.003124878 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -40.003124878 + -0.5 n = -40.003124878 + -0.5 Combine like terms: -40.003124878 + -0.5 = -40.503124878 n = -40.503124878 Simplifying n = -40.503124878Solution
The solution to the problem is based on the solutions from the subproblems. n = {39.503124878, -40.503124878}
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