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Simplifying n2 + -12n = 5 Reorder the terms: -12n + n2 = 5 Solving -12n + n2 = 5 Solving for variable 'n'. Reorder the terms: -5 + -12n + n2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -12n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -12n + 5 + n2 = 0 + 5 Reorder the terms: -5 + 5 + -12n + n2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -12n + n2 = 0 + 5 -12n + n2 = 0 + 5 Combine like terms: 0 + 5 = 5 -12n + n2 = 5 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 = 5 + 36 Reorder the terms: 36 + -12n + n2 = 5 + 36 Combine like terms: 5 + 36 = 41 36 + -12n + n2 = 41 Factor a perfect square on the left side: (n + -6)(n + -6) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (n + -6) equal to 6.403124237 and -6.403124237.Subproblem 1
n + -6 = 6.403124237 Simplifying n + -6 = 6.403124237 Reorder the terms: -6 + n = 6.403124237 Solving -6 + n = 6.403124237 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 = 6.403124237 + 6 Combine like terms: -6 + 6 = 0 0 + n = 6.403124237 + 6 n = 6.403124237 + 6 Combine like terms: 6.403124237 + 6 = 12.403124237 n = 12.403124237 Simplifying n = 12.403124237Subproblem 2
n + -6 = -6.403124237 Simplifying n + -6 = -6.403124237 Reorder the terms: -6 + n = -6.403124237 Solving -6 + n = -6.403124237 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 = -6.403124237 + 6 Combine like terms: -6 + 6 = 0 0 + n = -6.403124237 + 6 n = -6.403124237 + 6 Combine like terms: -6.403124237 + 6 = -0.403124237 n = -0.403124237 Simplifying n = -0.403124237Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.403124237, -0.403124237}
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