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Simplifying n2 + -12n = 35 Reorder the terms: -12n + n2 = 35 Solving -12n + n2 = 35 Solving for variable 'n'. Reorder the terms: -35 + -12n + n2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -12n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -12n + 35 + n2 = 0 + 35 Reorder the terms: -35 + 35 + -12n + n2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -12n + n2 = 0 + 35 -12n + n2 = 0 + 35 Combine like terms: 0 + 35 = 35 -12n + n2 = 35 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 = 35 + 36 Reorder the terms: 36 + -12n + n2 = 35 + 36 Combine like terms: 35 + 36 = 71 36 + -12n + n2 = 71 Factor a perfect square on the left side: (n + -6)(n + -6) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (n + -6) equal to 8.426149773 and -8.426149773.Subproblem 1
n + -6 = 8.426149773 Simplifying n + -6 = 8.426149773 Reorder the terms: -6 + n = 8.426149773 Solving -6 + n = 8.426149773 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 = 8.426149773 + 6 Combine like terms: -6 + 6 = 0 0 + n = 8.426149773 + 6 n = 8.426149773 + 6 Combine like terms: 8.426149773 + 6 = 14.426149773 n = 14.426149773 Simplifying n = 14.426149773Subproblem 2
n + -6 = -8.426149773 Simplifying n + -6 = -8.426149773 Reorder the terms: -6 + n = -8.426149773 Solving -6 + n = -8.426149773 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 = -8.426149773 + 6 Combine like terms: -6 + 6 = 0 0 + n = -8.426149773 + 6 n = -8.426149773 + 6 Combine like terms: -8.426149773 + 6 = -2.426149773 n = -2.426149773 Simplifying n = -2.426149773Solution
The solution to the problem is based on the solutions from the subproblems. n = {14.426149773, -2.426149773}
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