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Simplifying n2 + n = 4200 Reorder the terms: n + n2 = 4200 Solving n + n2 = 4200 Solving for variable 'n'. Reorder the terms: -4200 + n + n2 = 4200 + -4200 Combine like terms: 4200 + -4200 = 0 -4200 + n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '4200' to each side of the equation. -4200 + n + 4200 + n2 = 0 + 4200 Reorder the terms: -4200 + 4200 + n + n2 = 0 + 4200 Combine like terms: -4200 + 4200 = 0 0 + n + n2 = 0 + 4200 n + n2 = 0 + 4200 Combine like terms: 0 + 4200 = 4200 n + n2 = 4200 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 = 4200 + 0.25 Reorder the terms: 0.25 + n + n2 = 4200 + 0.25 Combine like terms: 4200 + 0.25 = 4200.25 0.25 + n + n2 = 4200.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 4200.25 Calculate the square root of the right side: 64.809335747 Break this problem into two subproblems by setting (n + 0.5) equal to 64.809335747 and -64.809335747.Subproblem 1
n + 0.5 = 64.809335747 Simplifying n + 0.5 = 64.809335747 Reorder the terms: 0.5 + n = 64.809335747 Solving 0.5 + n = 64.809335747 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 = 64.809335747 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 64.809335747 + -0.5 n = 64.809335747 + -0.5 Combine like terms: 64.809335747 + -0.5 = 64.309335747 n = 64.309335747 Simplifying n = 64.309335747Subproblem 2
n + 0.5 = -64.809335747 Simplifying n + 0.5 = -64.809335747 Reorder the terms: 0.5 + n = -64.809335747 Solving 0.5 + n = -64.809335747 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 = -64.809335747 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -64.809335747 + -0.5 n = -64.809335747 + -0.5 Combine like terms: -64.809335747 + -0.5 = -65.309335747 n = -65.309335747 Simplifying n = -65.309335747Solution
The solution to the problem is based on the solutions from the subproblems. n = {64.309335747, -65.309335747}
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