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Simplifying n2 + -4n + -54 = 0 Reorder the terms: -54 + -4n + n2 = 0 Solving -54 + -4n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + -4n + 54 + n2 = 0 + 54 Reorder the terms: -54 + 54 + -4n + n2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -4n + n2 = 0 + 54 -4n + n2 = 0 + 54 Combine like terms: 0 + 54 = 54 -4n + n2 = 54 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = 54 + 4 Reorder the terms: 4 + -4n + n2 = 54 + 4 Combine like terms: 54 + 4 = 58 4 + -4n + n2 = 58 Factor a perfect square on the left side: (n + -2)(n + -2) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (n + -2) equal to 7.615773106 and -7.615773106.Subproblem 1
n + -2 = 7.615773106 Simplifying n + -2 = 7.615773106 Reorder the terms: -2 + n = 7.615773106 Solving -2 + n = 7.615773106 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 7.615773106 + 2 Combine like terms: -2 + 2 = 0 0 + n = 7.615773106 + 2 n = 7.615773106 + 2 Combine like terms: 7.615773106 + 2 = 9.615773106 n = 9.615773106 Simplifying n = 9.615773106Subproblem 2
n + -2 = -7.615773106 Simplifying n + -2 = -7.615773106 Reorder the terms: -2 + n = -7.615773106 Solving -2 + n = -7.615773106 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = -7.615773106 + 2 Combine like terms: -2 + 2 = 0 0 + n = -7.615773106 + 2 n = -7.615773106 + 2 Combine like terms: -7.615773106 + 2 = -5.615773106 n = -5.615773106 Simplifying n = -5.615773106Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.615773106, -5.615773106}
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