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Simplifying n2 + -14n + -73 = 4 Reorder the terms: -73 + -14n + n2 = 4 Solving -73 + -14n + n2 = 4 Solving for variable 'n'. Reorder the terms: -73 + -4 + -14n + n2 = 4 + -4 Combine like terms: -73 + -4 = -77 -77 + -14n + n2 = 4 + -4 Combine like terms: 4 + -4 = 0 -77 + -14n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + -14n + 77 + n2 = 0 + 77 Reorder the terms: -77 + 77 + -14n + n2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + -14n + n2 = 0 + 77 -14n + n2 = 0 + 77 Combine like terms: 0 + 77 = 77 -14n + n2 = 77 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 = 77 + 49 Reorder the terms: 49 + -14n + n2 = 77 + 49 Combine like terms: 77 + 49 = 126 49 + -14n + n2 = 126 Factor a perfect square on the left side: (n + -7)(n + -7) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (n + -7) equal to 11.22497216 and -11.22497216.Subproblem 1
n + -7 = 11.22497216 Simplifying n + -7 = 11.22497216 Reorder the terms: -7 + n = 11.22497216 Solving -7 + n = 11.22497216 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 = 11.22497216 + 7 Combine like terms: -7 + 7 = 0 0 + n = 11.22497216 + 7 n = 11.22497216 + 7 Combine like terms: 11.22497216 + 7 = 18.22497216 n = 18.22497216 Simplifying n = 18.22497216Subproblem 2
n + -7 = -11.22497216 Simplifying n + -7 = -11.22497216 Reorder the terms: -7 + n = -11.22497216 Solving -7 + n = -11.22497216 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 = -11.22497216 + 7 Combine like terms: -7 + 7 = 0 0 + n = -11.22497216 + 7 n = -11.22497216 + 7 Combine like terms: -11.22497216 + 7 = -4.22497216 n = -4.22497216 Simplifying n = -4.22497216Solution
The solution to the problem is based on the solutions from the subproblems. n = {18.22497216, -4.22497216}
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