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Simplifying n2 + -1n + -66 = 0 Reorder the terms: -66 + -1n + n2 = 0 Solving -66 + -1n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + -1n + 66 + n2 = 0 + 66 Reorder the terms: -66 + 66 + -1n + n2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + -1n + n2 = 0 + 66 -1n + n2 = 0 + 66 Combine like terms: 0 + 66 = 66 -1n + n2 = 66 The n term is -1n. 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. -1n + 0.25 + n2 = 66 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 66 + 0.25 Combine like terms: 66 + 0.25 = 66.25 0.25 + -1n + n2 = 66.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (n + -0.5) equal to 8.139410298 and -8.139410298.Subproblem 1
n + -0.5 = 8.139410298 Simplifying n + -0.5 = 8.139410298 Reorder the terms: -0.5 + n = 8.139410298 Solving -0.5 + n = 8.139410298 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 = 8.139410298 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 8.139410298 + 0.5 n = 8.139410298 + 0.5 Combine like terms: 8.139410298 + 0.5 = 8.639410298 n = 8.639410298 Simplifying n = 8.639410298Subproblem 2
n + -0.5 = -8.139410298 Simplifying n + -0.5 = -8.139410298 Reorder the terms: -0.5 + n = -8.139410298 Solving -0.5 + n = -8.139410298 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 = -8.139410298 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -8.139410298 + 0.5 n = -8.139410298 + 0.5 Combine like terms: -8.139410298 + 0.5 = -7.639410298 n = -7.639410298 Simplifying n = -7.639410298Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.639410298, -7.639410298}
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