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Simplifying n2 + n + -6 = 25 Reorder the terms: -6 + n + n2 = 25 Solving -6 + n + n2 = 25 Solving for variable 'n'. Reorder the terms: -6 + -25 + n + n2 = 25 + -25 Combine like terms: -6 + -25 = -31 -31 + n + n2 = 25 + -25 Combine like terms: 25 + -25 = 0 -31 + n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + n + 31 + n2 = 0 + 31 Reorder the terms: -31 + 31 + n + n2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + n + n2 = 0 + 31 n + n2 = 0 + 31 Combine like terms: 0 + 31 = 31 n + n2 = 31 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 = 31 + 0.25 Reorder the terms: 0.25 + n + n2 = 31 + 0.25 Combine like terms: 31 + 0.25 = 31.25 0.25 + n + n2 = 31.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (n + 0.5) equal to 5.590169944 and -5.590169944.Subproblem 1
n + 0.5 = 5.590169944 Simplifying n + 0.5 = 5.590169944 Reorder the terms: 0.5 + n = 5.590169944 Solving 0.5 + n = 5.590169944 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 = 5.590169944 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 5.590169944 + -0.5 n = 5.590169944 + -0.5 Combine like terms: 5.590169944 + -0.5 = 5.090169944 n = 5.090169944 Simplifying n = 5.090169944Subproblem 2
n + 0.5 = -5.590169944 Simplifying n + 0.5 = -5.590169944 Reorder the terms: 0.5 + n = -5.590169944 Solving 0.5 + n = -5.590169944 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 = -5.590169944 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -5.590169944 + -0.5 n = -5.590169944 + -0.5 Combine like terms: -5.590169944 + -0.5 = -6.090169944 n = -6.090169944 Simplifying n = -6.090169944Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.090169944, -6.090169944}
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