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Simplifying -1n2 + -2n + -13 = -9n2 + 9n Reorder the terms: -13 + -2n + -1n2 = -9n2 + 9n Reorder the terms: -13 + -2n + -1n2 = 9n + -9n2 Solving -13 + -2n + -1n2 = 9n + -9n2 Solving for variable 'n'. Reorder the terms: -13 + -2n + -9n + -1n2 + 9n2 = 9n + -9n2 + -9n + 9n2 Combine like terms: -2n + -9n = -11n -13 + -11n + -1n2 + 9n2 = 9n + -9n2 + -9n + 9n2 Combine like terms: -1n2 + 9n2 = 8n2 -13 + -11n + 8n2 = 9n + -9n2 + -9n + 9n2 Reorder the terms: -13 + -11n + 8n2 = 9n + -9n + -9n2 + 9n2 Combine like terms: 9n + -9n = 0 -13 + -11n + 8n2 = 0 + -9n2 + 9n2 -13 + -11n + 8n2 = -9n2 + 9n2 Combine like terms: -9n2 + 9n2 = 0 -13 + -11n + 8n2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.625 + -1.375n + n2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + -1.375n + 1.625 + n2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + -1.375n + n2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + -1.375n + n2 = 0 + 1.625 -1.375n + n2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 -1.375n + n2 = 1.625 The n term is -1.375n. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375n + 0.47265625 + n2 = 1.625 + 0.47265625 Reorder the terms: 0.47265625 + -1.375n + n2 = 1.625 + 0.47265625 Combine like terms: 1.625 + 0.47265625 = 2.09765625 0.47265625 + -1.375n + n2 = 2.09765625 Factor a perfect square on the left side: (n + -0.6875)(n + -0.6875) = 2.09765625 Calculate the square root of the right side: 1.448328778 Break this problem into two subproblems by setting (n + -0.6875) equal to 1.448328778 and -1.448328778.Subproblem 1
n + -0.6875 = 1.448328778 Simplifying n + -0.6875 = 1.448328778 Reorder the terms: -0.6875 + n = 1.448328778 Solving -0.6875 + n = 1.448328778 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + n = 1.448328778 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + n = 1.448328778 + 0.6875 n = 1.448328778 + 0.6875 Combine like terms: 1.448328778 + 0.6875 = 2.135828778 n = 2.135828778 Simplifying n = 2.135828778Subproblem 2
n + -0.6875 = -1.448328778 Simplifying n + -0.6875 = -1.448328778 Reorder the terms: -0.6875 + n = -1.448328778 Solving -0.6875 + n = -1.448328778 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + n = -1.448328778 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + n = -1.448328778 + 0.6875 n = -1.448328778 + 0.6875 Combine like terms: -1.448328778 + 0.6875 = -0.760828778 n = -0.760828778 Simplifying n = -0.760828778Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.135828778, -0.760828778}
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