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Simplifying n2 + -14n + -40 = 0 Reorder the terms: -40 + -14n + n2 = 0 Solving -40 + -14n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -14n + 40 + n2 = 0 + 40 Reorder the terms: -40 + 40 + -14n + n2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -14n + n2 = 0 + 40 -14n + n2 = 0 + 40 Combine like terms: 0 + 40 = 40 -14n + n2 = 40 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 = 40 + 49 Reorder the terms: 49 + -14n + n2 = 40 + 49 Combine like terms: 40 + 49 = 89 49 + -14n + n2 = 89 Factor a perfect square on the left side: (n + -7)(n + -7) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (n + -7) equal to 9.433981132 and -9.433981132.Subproblem 1
n + -7 = 9.433981132 Simplifying n + -7 = 9.433981132 Reorder the terms: -7 + n = 9.433981132 Solving -7 + n = 9.433981132 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 = 9.433981132 + 7 Combine like terms: -7 + 7 = 0 0 + n = 9.433981132 + 7 n = 9.433981132 + 7 Combine like terms: 9.433981132 + 7 = 16.433981132 n = 16.433981132 Simplifying n = 16.433981132Subproblem 2
n + -7 = -9.433981132 Simplifying n + -7 = -9.433981132 Reorder the terms: -7 + n = -9.433981132 Solving -7 + n = -9.433981132 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 = -9.433981132 + 7 Combine like terms: -7 + 7 = 0 0 + n = -9.433981132 + 7 n = -9.433981132 + 7 Combine like terms: -9.433981132 + 7 = -2.433981132 n = -2.433981132 Simplifying n = -2.433981132Solution
The solution to the problem is based on the solutions from the subproblems. n = {16.433981132, -2.433981132}
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