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Simplifying n2 + -12n + 21 = 0 Reorder the terms: 21 + -12n + n2 = 0 Solving 21 + -12n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -12n + -21 + n2 = 0 + -21 Reorder the terms: 21 + -21 + -12n + n2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -12n + n2 = 0 + -21 -12n + n2 = 0 + -21 Combine like terms: 0 + -21 = -21 -12n + n2 = -21 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 = -21 + 36 Reorder the terms: 36 + -12n + n2 = -21 + 36 Combine like terms: -21 + 36 = 15 36 + -12n + n2 = 15 Factor a perfect square on the left side: (n + -6)(n + -6) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (n + -6) equal to 3.872983346 and -3.872983346.Subproblem 1
n + -6 = 3.872983346 Simplifying n + -6 = 3.872983346 Reorder the terms: -6 + n = 3.872983346 Solving -6 + n = 3.872983346 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 = 3.872983346 + 6 Combine like terms: -6 + 6 = 0 0 + n = 3.872983346 + 6 n = 3.872983346 + 6 Combine like terms: 3.872983346 + 6 = 9.872983346 n = 9.872983346 Simplifying n = 9.872983346Subproblem 2
n + -6 = -3.872983346 Simplifying n + -6 = -3.872983346 Reorder the terms: -6 + n = -3.872983346 Solving -6 + n = -3.872983346 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 = -3.872983346 + 6 Combine like terms: -6 + 6 = 0 0 + n = -3.872983346 + 6 n = -3.872983346 + 6 Combine like terms: -3.872983346 + 6 = 2.127016654 n = 2.127016654 Simplifying n = 2.127016654Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.872983346, 2.127016654}
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