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Simplifying -4n2 + 6n + -16 = -15n Reorder the terms: -16 + 6n + -4n2 = -15n Solving -16 + 6n + -4n2 = -15n Solving for variable 'n'. Reorder the terms: -16 + 6n + 15n + -4n2 = -15n + 15n Combine like terms: 6n + 15n = 21n -16 + 21n + -4n2 = -15n + 15n Combine like terms: -15n + 15n = 0 -16 + 21n + -4n2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 4 + -5.25n + n2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -5.25n + -4 + n2 = 0 + -4 Reorder the terms: 4 + -4 + -5.25n + n2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5.25n + n2 = 0 + -4 -5.25n + n2 = 0 + -4 Combine like terms: 0 + -4 = -4 -5.25n + n2 = -4 The n term is -5.25n. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25n + 6.890625 + n2 = -4 + 6.890625 Reorder the terms: 6.890625 + -5.25n + n2 = -4 + 6.890625 Combine like terms: -4 + 6.890625 = 2.890625 6.890625 + -5.25n + n2 = 2.890625 Factor a perfect square on the left side: (n + -2.625)(n + -2.625) = 2.890625 Calculate the square root of the right side: 1.700183814 Break this problem into two subproblems by setting (n + -2.625) equal to 1.700183814 and -1.700183814.Subproblem 1
n + -2.625 = 1.700183814 Simplifying n + -2.625 = 1.700183814 Reorder the terms: -2.625 + n = 1.700183814 Solving -2.625 + n = 1.700183814 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + n = 1.700183814 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + n = 1.700183814 + 2.625 n = 1.700183814 + 2.625 Combine like terms: 1.700183814 + 2.625 = 4.325183814 n = 4.325183814 Simplifying n = 4.325183814Subproblem 2
n + -2.625 = -1.700183814 Simplifying n + -2.625 = -1.700183814 Reorder the terms: -2.625 + n = -1.700183814 Solving -2.625 + n = -1.700183814 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + n = -1.700183814 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + n = -1.700183814 + 2.625 n = -1.700183814 + 2.625 Combine like terms: -1.700183814 + 2.625 = 0.924816186 n = 0.924816186 Simplifying n = 0.924816186Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.325183814, 0.924816186}
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