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Simplifying n2 + -14n = 29 Reorder the terms: -14n + n2 = 29 Solving -14n + n2 = 29 Solving for variable 'n'. Reorder the terms: -29 + -14n + n2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + -14n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -14n + 29 + n2 = 0 + 29 Reorder the terms: -29 + 29 + -14n + n2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -14n + n2 = 0 + 29 -14n + n2 = 0 + 29 Combine like terms: 0 + 29 = 29 -14n + n2 = 29 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 = 29 + 49 Reorder the terms: 49 + -14n + n2 = 29 + 49 Combine like terms: 29 + 49 = 78 49 + -14n + n2 = 78 Factor a perfect square on the left side: (n + -7)(n + -7) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (n + -7) equal to 8.831760866 and -8.831760866.Subproblem 1
n + -7 = 8.831760866 Simplifying n + -7 = 8.831760866 Reorder the terms: -7 + n = 8.831760866 Solving -7 + n = 8.831760866 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 = 8.831760866 + 7 Combine like terms: -7 + 7 = 0 0 + n = 8.831760866 + 7 n = 8.831760866 + 7 Combine like terms: 8.831760866 + 7 = 15.831760866 n = 15.831760866 Simplifying n = 15.831760866Subproblem 2
n + -7 = -8.831760866 Simplifying n + -7 = -8.831760866 Reorder the terms: -7 + n = -8.831760866 Solving -7 + n = -8.831760866 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 = -8.831760866 + 7 Combine like terms: -7 + 7 = 0 0 + n = -8.831760866 + 7 n = -8.831760866 + 7 Combine like terms: -8.831760866 + 7 = -1.831760866 n = -1.831760866 Simplifying n = -1.831760866Solution
The solution to the problem is based on the solutions from the subproblems. n = {15.831760866, -1.831760866}
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