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Simplifying n2 + 14n + -43 = 0 Reorder the terms: -43 + 14n + n2 = 0 Solving -43 + 14n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 14n + 43 + n2 = 0 + 43 Reorder the terms: -43 + 43 + 14n + n2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 14n + n2 = 0 + 43 14n + n2 = 0 + 43 Combine like terms: 0 + 43 = 43 14n + n2 = 43 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 = 43 + 49 Reorder the terms: 49 + 14n + n2 = 43 + 49 Combine like terms: 43 + 49 = 92 49 + 14n + n2 = 92 Factor a perfect square on the left side: (n + 7)(n + 7) = 92 Calculate the square root of the right side: 9.591663047 Break this problem into two subproblems by setting (n + 7) equal to 9.591663047 and -9.591663047.Subproblem 1
n + 7 = 9.591663047 Simplifying n + 7 = 9.591663047 Reorder the terms: 7 + n = 9.591663047 Solving 7 + n = 9.591663047 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 = 9.591663047 + -7 Combine like terms: 7 + -7 = 0 0 + n = 9.591663047 + -7 n = 9.591663047 + -7 Combine like terms: 9.591663047 + -7 = 2.591663047 n = 2.591663047 Simplifying n = 2.591663047Subproblem 2
n + 7 = -9.591663047 Simplifying n + 7 = -9.591663047 Reorder the terms: 7 + n = -9.591663047 Solving 7 + n = -9.591663047 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 = -9.591663047 + -7 Combine like terms: 7 + -7 = 0 0 + n = -9.591663047 + -7 n = -9.591663047 + -7 Combine like terms: -9.591663047 + -7 = -16.591663047 n = -16.591663047 Simplifying n = -16.591663047Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.591663047, -16.591663047}
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