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Simplifying 9n2 + -5 = 9n Reorder the terms: -5 + 9n2 = 9n Solving -5 + 9n2 = 9n Solving for variable 'n'. Reorder the terms: -5 + -9n + 9n2 = 9n + -9n Combine like terms: 9n + -9n = 0 -5 + -9n + 9n2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + -1n + n2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -1n + 0.5555555556 + n2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -1n + n2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -1n + n2 = 0 + 0.5555555556 -1n + n2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -1n + n2 = 0.5555555556 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 = 0.5555555556 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 0.5555555556 + 0.25 Combine like terms: 0.5555555556 + 0.25 = 0.8055555556 0.25 + -1n + n2 = 0.8055555556 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 0.8055555556 Calculate the square root of the right side: 0.897527468 Break this problem into two subproblems by setting (n + -0.5) equal to 0.897527468 and -0.897527468.Subproblem 1
n + -0.5 = 0.897527468 Simplifying n + -0.5 = 0.897527468 Reorder the terms: -0.5 + n = 0.897527468 Solving -0.5 + n = 0.897527468 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 = 0.897527468 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 0.897527468 + 0.5 n = 0.897527468 + 0.5 Combine like terms: 0.897527468 + 0.5 = 1.397527468 n = 1.397527468 Simplifying n = 1.397527468Subproblem 2
n + -0.5 = -0.897527468 Simplifying n + -0.5 = -0.897527468 Reorder the terms: -0.5 + n = -0.897527468 Solving -0.5 + n = -0.897527468 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 = -0.897527468 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -0.897527468 + 0.5 n = -0.897527468 + 0.5 Combine like terms: -0.897527468 + 0.5 = -0.397527468 n = -0.397527468 Simplifying n = -0.397527468Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.397527468, -0.397527468}
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