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Simplifying n2 + -4n + -14 = -5 Reorder the terms: -14 + -4n + n2 = -5 Solving -14 + -4n + n2 = -5 Solving for variable 'n'. Reorder the terms: -14 + 5 + -4n + n2 = -5 + 5 Combine like terms: -14 + 5 = -9 -9 + -4n + n2 = -5 + 5 Combine like terms: -5 + 5 = 0 -9 + -4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -4n + 9 + n2 = 0 + 9 Reorder the terms: -9 + 9 + -4n + n2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4n + n2 = 0 + 9 -4n + n2 = 0 + 9 Combine like terms: 0 + 9 = 9 -4n + n2 = 9 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 = 9 + 4 Reorder the terms: 4 + -4n + n2 = 9 + 4 Combine like terms: 9 + 4 = 13 4 + -4n + n2 = 13 Factor a perfect square on the left side: (n + -2)(n + -2) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (n + -2) equal to 3.605551275 and -3.605551275.Subproblem 1
n + -2 = 3.605551275 Simplifying n + -2 = 3.605551275 Reorder the terms: -2 + n = 3.605551275 Solving -2 + n = 3.605551275 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 = 3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + n = 3.605551275 + 2 n = 3.605551275 + 2 Combine like terms: 3.605551275 + 2 = 5.605551275 n = 5.605551275 Simplifying n = 5.605551275Subproblem 2
n + -2 = -3.605551275 Simplifying n + -2 = -3.605551275 Reorder the terms: -2 + n = -3.605551275 Solving -2 + n = -3.605551275 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 = -3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + n = -3.605551275 + 2 n = -3.605551275 + 2 Combine like terms: -3.605551275 + 2 = -1.605551275 n = -1.605551275 Simplifying n = -1.605551275Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.605551275, -1.605551275}
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