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Simplifying 9n2 + -5n + -6 = 0 Reorder the terms: -6 + -5n + 9n2 = 0 Solving -6 + -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'. -0.6666666667 + -0.5555555556n + n2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -0.5555555556n + 0.6666666667 + n2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -0.5555555556n + n2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -0.5555555556n + n2 = 0 + 0.6666666667 -0.5555555556n + n2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -0.5555555556n + n2 = 0.6666666667 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 = 0.6666666667 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556n + n2 = 0.6666666667 + 0.07716049384 Combine like terms: 0.6666666667 + 0.07716049384 = 0.74382716054 0.07716049384 + -0.5555555556n + n2 = 0.74382716054 Factor a perfect square on the left side: (n + -0.2777777778)(n + -0.2777777778) = 0.74382716054 Calculate the square root of the right side: 0.86245415 Break this problem into two subproblems by setting (n + -0.2777777778) equal to 0.86245415 and -0.86245415.Subproblem 1
n + -0.2777777778 = 0.86245415 Simplifying n + -0.2777777778 = 0.86245415 Reorder the terms: -0.2777777778 + n = 0.86245415 Solving -0.2777777778 + n = 0.86245415 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 = 0.86245415 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + n = 0.86245415 + 0.2777777778 n = 0.86245415 + 0.2777777778 Combine like terms: 0.86245415 + 0.2777777778 = 1.1402319278 n = 1.1402319278 Simplifying n = 1.1402319278Subproblem 2
n + -0.2777777778 = -0.86245415 Simplifying n + -0.2777777778 = -0.86245415 Reorder the terms: -0.2777777778 + n = -0.86245415 Solving -0.2777777778 + n = -0.86245415 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 = -0.86245415 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + n = -0.86245415 + 0.2777777778 n = -0.86245415 + 0.2777777778 Combine like terms: -0.86245415 + 0.2777777778 = -0.5846763722 n = -0.5846763722 Simplifying n = -0.5846763722Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.1402319278, -0.5846763722}
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