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Simplifying n2 + -5n + -25 = 0 Reorder the terms: -25 + -5n + n2 = 0 Solving -25 + -5n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -5n + 25 + n2 = 0 + 25 Reorder the terms: -25 + 25 + -5n + n2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -5n + n2 = 0 + 25 -5n + n2 = 0 + 25 Combine like terms: 0 + 25 = 25 -5n + n2 = 25 The n term is -5n. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5n + 6.25 + n2 = 25 + 6.25 Reorder the terms: 6.25 + -5n + n2 = 25 + 6.25 Combine like terms: 25 + 6.25 = 31.25 6.25 + -5n + n2 = 31.25 Factor a perfect square on the left side: (n + -2.5)(n + -2.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (n + -2.5) equal to 5.590169944 and -5.590169944.Subproblem 1
n + -2.5 = 5.590169944 Simplifying n + -2.5 = 5.590169944 Reorder the terms: -2.5 + n = 5.590169944 Solving -2.5 + n = 5.590169944 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = 5.590169944 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = 5.590169944 + 2.5 n = 5.590169944 + 2.5 Combine like terms: 5.590169944 + 2.5 = 8.090169944 n = 8.090169944 Simplifying n = 8.090169944Subproblem 2
n + -2.5 = -5.590169944 Simplifying n + -2.5 = -5.590169944 Reorder the terms: -2.5 + n = -5.590169944 Solving -2.5 + n = -5.590169944 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = -5.590169944 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = -5.590169944 + 2.5 n = -5.590169944 + 2.5 Combine like terms: -5.590169944 + 2.5 = -3.090169944 n = -3.090169944 Simplifying n = -3.090169944Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.090169944, -3.090169944}
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