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Simplifying n2 + -6n + -78 = -4 Reorder the terms: -78 + -6n + n2 = -4 Solving -78 + -6n + n2 = -4 Solving for variable 'n'. Reorder the terms: -78 + 4 + -6n + n2 = -4 + 4 Combine like terms: -78 + 4 = -74 -74 + -6n + n2 = -4 + 4 Combine like terms: -4 + 4 = 0 -74 + -6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + -6n + 74 + n2 = 0 + 74 Reorder the terms: -74 + 74 + -6n + n2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + -6n + n2 = 0 + 74 -6n + n2 = 0 + 74 Combine like terms: 0 + 74 = 74 -6n + n2 = 74 The n term is -6n. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6n + 9 + n2 = 74 + 9 Reorder the terms: 9 + -6n + n2 = 74 + 9 Combine like terms: 74 + 9 = 83 9 + -6n + n2 = 83 Factor a perfect square on the left side: (n + -3)(n + -3) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (n + -3) equal to 9.110433579 and -9.110433579.Subproblem 1
n + -3 = 9.110433579 Simplifying n + -3 = 9.110433579 Reorder the terms: -3 + n = 9.110433579 Solving -3 + n = 9.110433579 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = 9.110433579 + 3 Combine like terms: -3 + 3 = 0 0 + n = 9.110433579 + 3 n = 9.110433579 + 3 Combine like terms: 9.110433579 + 3 = 12.110433579 n = 12.110433579 Simplifying n = 12.110433579Subproblem 2
n + -3 = -9.110433579 Simplifying n + -3 = -9.110433579 Reorder the terms: -3 + n = -9.110433579 Solving -3 + n = -9.110433579 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = -9.110433579 + 3 Combine like terms: -3 + 3 = 0 0 + n = -9.110433579 + 3 n = -9.110433579 + 3 Combine like terms: -9.110433579 + 3 = -6.110433579 n = -6.110433579 Simplifying n = -6.110433579Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.110433579, -6.110433579}
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