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Simplifying 126 = 6n2 + n + -1 Reorder the terms: 126 = -1 + n + 6n2 Solving 126 = -1 + n + 6n2 Solving for variable 'n'. Combine like terms: 126 + 1 = 127 127 + -1n + -6n2 = -1 + n + 6n2 + 1 + -1n + -6n2 Reorder the terms: 127 + -1n + -6n2 = -1 + 1 + n + -1n + 6n2 + -6n2 Combine like terms: -1 + 1 = 0 127 + -1n + -6n2 = 0 + n + -1n + 6n2 + -6n2 127 + -1n + -6n2 = n + -1n + 6n2 + -6n2 Combine like terms: n + -1n = 0 127 + -1n + -6n2 = 0 + 6n2 + -6n2 127 + -1n + -6n2 = 6n2 + -6n2 Combine like terms: 6n2 + -6n2 = 0 127 + -1n + -6n2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -21.16666667 + 0.1666666667n + n2 = 0 Move the constant term to the right: Add '21.16666667' to each side of the equation. -21.16666667 + 0.1666666667n + 21.16666667 + n2 = 0 + 21.16666667 Reorder the terms: -21.16666667 + 21.16666667 + 0.1666666667n + n2 = 0 + 21.16666667 Combine like terms: -21.16666667 + 21.16666667 = 0.00000000 0.00000000 + 0.1666666667n + n2 = 0 + 21.16666667 0.1666666667n + n2 = 0 + 21.16666667 Combine like terms: 0 + 21.16666667 = 21.16666667 0.1666666667n + n2 = 21.16666667 The n term is 0.1666666667n. Take half its coefficient (0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. 0.1666666667n + 0.006944444447 + n2 = 21.16666667 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667n + n2 = 21.16666667 + 0.006944444447 Combine like terms: 21.16666667 + 0.006944444447 = 21.173611114447 0.006944444447 + 0.1666666667n + n2 = 21.173611114447 Factor a perfect square on the left side: (n + 0.08333333335)(n + 0.08333333335) = 21.173611114447 Calculate the square root of the right side: 4.601479231 Break this problem into two subproblems by setting (n + 0.08333333335) equal to 4.601479231 and -4.601479231.Subproblem 1
n + 0.08333333335 = 4.601479231 Simplifying n + 0.08333333335 = 4.601479231 Reorder the terms: 0.08333333335 + n = 4.601479231 Solving 0.08333333335 + n = 4.601479231 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + n = 4.601479231 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + n = 4.601479231 + -0.08333333335 n = 4.601479231 + -0.08333333335 Combine like terms: 4.601479231 + -0.08333333335 = 4.51814589765 n = 4.51814589765 Simplifying n = 4.51814589765Subproblem 2
n + 0.08333333335 = -4.601479231 Simplifying n + 0.08333333335 = -4.601479231 Reorder the terms: 0.08333333335 + n = -4.601479231 Solving 0.08333333335 + n = -4.601479231 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + n = -4.601479231 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + n = -4.601479231 + -0.08333333335 n = -4.601479231 + -0.08333333335 Combine like terms: -4.601479231 + -0.08333333335 = -4.68481256435 n = -4.68481256435 Simplifying n = -4.68481256435Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.51814589765, -4.68481256435}
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