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Simplifying n2 + -21 = 14n Reorder the terms: -21 + n2 = 14n Solving -21 + n2 = 14n Solving for variable 'n'. Reorder the terms: -21 + -14n + n2 = 14n + -14n Combine like terms: 14n + -14n = 0 -21 + -14n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -14n + 21 + n2 = 0 + 21 Reorder the terms: -21 + 21 + -14n + n2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -14n + n2 = 0 + 21 -14n + n2 = 0 + 21 Combine like terms: 0 + 21 = 21 -14n + n2 = 21 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 = 21 + 49 Reorder the terms: 49 + -14n + n2 = 21 + 49 Combine like terms: 21 + 49 = 70 49 + -14n + n2 = 70 Factor a perfect square on the left side: (n + -7)(n + -7) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (n + -7) equal to 8.366600265 and -8.366600265.Subproblem 1
n + -7 = 8.366600265 Simplifying n + -7 = 8.366600265 Reorder the terms: -7 + n = 8.366600265 Solving -7 + n = 8.366600265 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 = 8.366600265 + 7 Combine like terms: -7 + 7 = 0 0 + n = 8.366600265 + 7 n = 8.366600265 + 7 Combine like terms: 8.366600265 + 7 = 15.366600265 n = 15.366600265 Simplifying n = 15.366600265Subproblem 2
n + -7 = -8.366600265 Simplifying n + -7 = -8.366600265 Reorder the terms: -7 + n = -8.366600265 Solving -7 + n = -8.366600265 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 = -8.366600265 + 7 Combine like terms: -7 + 7 = 0 0 + n = -8.366600265 + 7 n = -8.366600265 + 7 Combine like terms: -8.366600265 + 7 = -1.366600265 n = -1.366600265 Simplifying n = -1.366600265Solution
The solution to the problem is based on the solutions from the subproblems. n = {15.366600265, -1.366600265}
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