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Simplifying 9n2 + -5n + -9 = 0 Reorder the terms: -9 + -5n + 9n2 = 0 Solving -9 + -5n + 9n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1 + -0.5555555556n + n2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.5555555556n + 1 + n2 = 0 + 1 Reorder the terms: -1 + 1 + -0.5555555556n + n2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.5555555556n + n2 = 0 + 1 -0.5555555556n + n2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.5555555556n + n2 = 1 The n term is -0.5555555556n. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556n + 0.07716049384 + n2 = 1 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556n + n2 = 1 + 0.07716049384 Combine like terms: 1 + 0.07716049384 = 1.07716049384 0.07716049384 + -0.5555555556n + n2 = 1.07716049384 Factor a perfect square on the left side: (n + -0.2777777778)(n + -0.2777777778) = 1.07716049384 Calculate the square root of the right side: 1.037863427 Break this problem into two subproblems by setting (n + -0.2777777778) equal to 1.037863427 and -1.037863427.Subproblem 1
n + -0.2777777778 = 1.037863427 Simplifying n + -0.2777777778 = 1.037863427 Reorder the terms: -0.2777777778 + n = 1.037863427 Solving -0.2777777778 + n = 1.037863427 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + n = 1.037863427 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + n = 1.037863427 + 0.2777777778 n = 1.037863427 + 0.2777777778 Combine like terms: 1.037863427 + 0.2777777778 = 1.3156412048 n = 1.3156412048 Simplifying n = 1.3156412048Subproblem 2
n + -0.2777777778 = -1.037863427 Simplifying n + -0.2777777778 = -1.037863427 Reorder the terms: -0.2777777778 + n = -1.037863427 Solving -0.2777777778 + n = -1.037863427 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + n = -1.037863427 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + n = -1.037863427 + 0.2777777778 n = -1.037863427 + 0.2777777778 Combine like terms: -1.037863427 + 0.2777777778 = -0.7600856492 n = -0.7600856492 Simplifying n = -0.7600856492Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.3156412048, -0.7600856492}
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