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Simplifying n2 + -12n + -202 = 8 Reorder the terms: -202 + -12n + n2 = 8 Solving -202 + -12n + n2 = 8 Solving for variable 'n'. Reorder the terms: -202 + -8 + -12n + n2 = 8 + -8 Combine like terms: -202 + -8 = -210 -210 + -12n + n2 = 8 + -8 Combine like terms: 8 + -8 = 0 -210 + -12n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '210' to each side of the equation. -210 + -12n + 210 + n2 = 0 + 210 Reorder the terms: -210 + 210 + -12n + n2 = 0 + 210 Combine like terms: -210 + 210 = 0 0 + -12n + n2 = 0 + 210 -12n + n2 = 0 + 210 Combine like terms: 0 + 210 = 210 -12n + n2 = 210 The n term is -12n. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12n + 36 + n2 = 210 + 36 Reorder the terms: 36 + -12n + n2 = 210 + 36 Combine like terms: 210 + 36 = 246 36 + -12n + n2 = 246 Factor a perfect square on the left side: (n + -6)(n + -6) = 246 Calculate the square root of the right side: 15.684387141 Break this problem into two subproblems by setting (n + -6) equal to 15.684387141 and -15.684387141.Subproblem 1
n + -6 = 15.684387141 Simplifying n + -6 = 15.684387141 Reorder the terms: -6 + n = 15.684387141 Solving -6 + n = 15.684387141 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = 15.684387141 + 6 Combine like terms: -6 + 6 = 0 0 + n = 15.684387141 + 6 n = 15.684387141 + 6 Combine like terms: 15.684387141 + 6 = 21.684387141 n = 21.684387141 Simplifying n = 21.684387141Subproblem 2
n + -6 = -15.684387141 Simplifying n + -6 = -15.684387141 Reorder the terms: -6 + n = -15.684387141 Solving -6 + n = -15.684387141 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = -15.684387141 + 6 Combine like terms: -6 + 6 = 0 0 + n = -15.684387141 + 6 n = -15.684387141 + 6 Combine like terms: -15.684387141 + 6 = -9.684387141 n = -9.684387141 Simplifying n = -9.684387141Solution
The solution to the problem is based on the solutions from the subproblems. n = {21.684387141, -9.684387141}
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