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Simplifying n2 + n + -225 = 0 Reorder the terms: -225 + n + n2 = 0 Solving -225 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + n + 225 + n2 = 0 + 225 Reorder the terms: -225 + 225 + n + n2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + n + n2 = 0 + 225 n + n2 = 0 + 225 Combine like terms: 0 + 225 = 225 n + n2 = 225 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. n + 0.25 + n2 = 225 + 0.25 Reorder the terms: 0.25 + n + n2 = 225 + 0.25 Combine like terms: 225 + 0.25 = 225.25 0.25 + n + n2 = 225.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 225.25 Calculate the square root of the right side: 15.00833102 Break this problem into two subproblems by setting (n + 0.5) equal to 15.00833102 and -15.00833102.Subproblem 1
n + 0.5 = 15.00833102 Simplifying n + 0.5 = 15.00833102 Reorder the terms: 0.5 + n = 15.00833102 Solving 0.5 + n = 15.00833102 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 = 15.00833102 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 15.00833102 + -0.5 n = 15.00833102 + -0.5 Combine like terms: 15.00833102 + -0.5 = 14.50833102 n = 14.50833102 Simplifying n = 14.50833102Subproblem 2
n + 0.5 = -15.00833102 Simplifying n + 0.5 = -15.00833102 Reorder the terms: 0.5 + n = -15.00833102 Solving 0.5 + n = -15.00833102 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 = -15.00833102 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -15.00833102 + -0.5 n = -15.00833102 + -0.5 Combine like terms: -15.00833102 + -0.5 = -15.50833102 n = -15.50833102 Simplifying n = -15.50833102Solution
The solution to the problem is based on the solutions from the subproblems. n = {14.50833102, -15.50833102}
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