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Simplifying -4n(2n + -6) + -1n = -9 Reorder the terms: -4n(-6 + 2n) + -1n = -9 (-6 * -4n + 2n * -4n) + -1n = -9 (24n + -8n2) + -1n = -9 Reorder the terms: 24n + -1n + -8n2 = -9 Combine like terms: 24n + -1n = 23n 23n + -8n2 = -9 Solving 23n + -8n2 = -9 Solving for variable 'n'. Reorder the terms: 9 + 23n + -8n2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + 23n + -8n2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.125 + -2.875n + n2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -2.875n + 1.125 + n2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -2.875n + n2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -2.875n + n2 = 0 + 1.125 -2.875n + n2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -2.875n + n2 = 1.125 The n term is -2.875n. Take half its coefficient (-1.4375). Square it (2.06640625) and add it to both sides. Add '2.06640625' to each side of the equation. -2.875n + 2.06640625 + n2 = 1.125 + 2.06640625 Reorder the terms: 2.06640625 + -2.875n + n2 = 1.125 + 2.06640625 Combine like terms: 1.125 + 2.06640625 = 3.19140625 2.06640625 + -2.875n + n2 = 3.19140625 Factor a perfect square on the left side: (n + -1.4375)(n + -1.4375) = 3.19140625 Calculate the square root of the right side: 1.786450741 Break this problem into two subproblems by setting (n + -1.4375) equal to 1.786450741 and -1.786450741.Subproblem 1
n + -1.4375 = 1.786450741 Simplifying n + -1.4375 = 1.786450741 Reorder the terms: -1.4375 + n = 1.786450741 Solving -1.4375 + n = 1.786450741 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + n = 1.786450741 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + n = 1.786450741 + 1.4375 n = 1.786450741 + 1.4375 Combine like terms: 1.786450741 + 1.4375 = 3.223950741 n = 3.223950741 Simplifying n = 3.223950741Subproblem 2
n + -1.4375 = -1.786450741 Simplifying n + -1.4375 = -1.786450741 Reorder the terms: -1.4375 + n = -1.786450741 Solving -1.4375 + n = -1.786450741 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + n = -1.786450741 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + n = -1.786450741 + 1.4375 n = -1.786450741 + 1.4375 Combine like terms: -1.786450741 + 1.4375 = -0.348950741 n = -0.348950741 Simplifying n = -0.348950741Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.223950741, -0.348950741}
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