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Simplifying n2 + -2n + -1n + -2 + -54 = 0 Reorder the terms: -2 + -54 + -2n + -1n + n2 = 0 Combine like terms: -2 + -54 = -56 -56 + -2n + -1n + n2 = 0 Combine like terms: -2n + -1n = -3n -56 + -3n + n2 = 0 Solving -56 + -3n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -3n + 56 + n2 = 0 + 56 Reorder the terms: -56 + 56 + -3n + n2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -3n + n2 = 0 + 56 -3n + n2 = 0 + 56 Combine like terms: 0 + 56 = 56 -3n + n2 = 56 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 56 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 56 + 2.25 Combine like terms: 56 + 2.25 = 58.25 2.25 + -3n + n2 = 58.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (n + -1.5) equal to 7.632168761 and -7.632168761.Subproblem 1
n + -1.5 = 7.632168761 Simplifying n + -1.5 = 7.632168761 Reorder the terms: -1.5 + n = 7.632168761 Solving -1.5 + n = 7.632168761 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 7.632168761 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 7.632168761 + 1.5 n = 7.632168761 + 1.5 Combine like terms: 7.632168761 + 1.5 = 9.132168761 n = 9.132168761 Simplifying n = 9.132168761Subproblem 2
n + -1.5 = -7.632168761 Simplifying n + -1.5 = -7.632168761 Reorder the terms: -1.5 + n = -7.632168761 Solving -1.5 + n = -7.632168761 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -7.632168761 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -7.632168761 + 1.5 n = -7.632168761 + 1.5 Combine like terms: -7.632168761 + 1.5 = -6.132168761 n = -6.132168761 Simplifying n = -6.132168761Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.132168761, -6.132168761}
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