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Simplifying n2 + 14n + -30 = 0 Reorder the terms: -30 + 14n + n2 = 0 Solving -30 + 14n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 14n + 30 + n2 = 0 + 30 Reorder the terms: -30 + 30 + 14n + n2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 14n + n2 = 0 + 30 14n + n2 = 0 + 30 Combine like terms: 0 + 30 = 30 14n + n2 = 30 The n term is 14n. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14n + 49 + n2 = 30 + 49 Reorder the terms: 49 + 14n + n2 = 30 + 49 Combine like terms: 30 + 49 = 79 49 + 14n + n2 = 79 Factor a perfect square on the left side: (n + 7)(n + 7) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (n + 7) equal to 8.888194417 and -8.888194417.Subproblem 1
n + 7 = 8.888194417 Simplifying n + 7 = 8.888194417 Reorder the terms: 7 + n = 8.888194417 Solving 7 + n = 8.888194417 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + n = 8.888194417 + -7 Combine like terms: 7 + -7 = 0 0 + n = 8.888194417 + -7 n = 8.888194417 + -7 Combine like terms: 8.888194417 + -7 = 1.888194417 n = 1.888194417 Simplifying n = 1.888194417Subproblem 2
n + 7 = -8.888194417 Simplifying n + 7 = -8.888194417 Reorder the terms: 7 + n = -8.888194417 Solving 7 + n = -8.888194417 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + n = -8.888194417 + -7 Combine like terms: 7 + -7 = 0 0 + n = -8.888194417 + -7 n = -8.888194417 + -7 Combine like terms: -8.888194417 + -7 = -15.888194417 n = -15.888194417 Simplifying n = -15.888194417Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.888194417, -15.888194417}
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