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Simplifying 9n2 = 9n + 16 Reorder the terms: 9n2 = 16 + 9n Solving 9n2 = 16 + 9n Solving for variable 'n'. Reorder the terms: -16 + -9n + 9n2 = 16 + 9n + -16 + -9n Reorder the terms: -16 + -9n + 9n2 = 16 + -16 + 9n + -9n Combine like terms: 16 + -16 = 0 -16 + -9n + 9n2 = 0 + 9n + -9n -16 + -9n + 9n2 = 9n + -9n Combine like terms: 9n + -9n = 0 -16 + -9n + 9n2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.777777778 + -1n + n2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -1n + 1.777777778 + n2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -1n + n2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -1n + n2 = 0 + 1.777777778 -1n + n2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -1n + n2 = 1.777777778 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 1.777777778 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 1.777777778 + 0.25 Combine like terms: 1.777777778 + 0.25 = 2.027777778 0.25 + -1n + n2 = 2.027777778 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 2.027777778 Calculate the square root of the right side: 1.424000624 Break this problem into two subproblems by setting (n + -0.5) equal to 1.424000624 and -1.424000624.Subproblem 1
n + -0.5 = 1.424000624 Simplifying n + -0.5 = 1.424000624 Reorder the terms: -0.5 + n = 1.424000624 Solving -0.5 + n = 1.424000624 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 1.424000624 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 1.424000624 + 0.5 n = 1.424000624 + 0.5 Combine like terms: 1.424000624 + 0.5 = 1.924000624 n = 1.924000624 Simplifying n = 1.924000624Subproblem 2
n + -0.5 = -1.424000624 Simplifying n + -0.5 = -1.424000624 Reorder the terms: -0.5 + n = -1.424000624 Solving -0.5 + n = -1.424000624 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -1.424000624 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -1.424000624 + 0.5 n = -1.424000624 + 0.5 Combine like terms: -1.424000624 + 0.5 = -0.924000624 n = -0.924000624 Simplifying n = -0.924000624Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.924000624, -0.924000624}
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