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Simplifying 2n2 + -21n + 11 = 0 Reorder the terms: 11 + -21n + 2n2 = 0 Solving 11 + -21n + 2n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + -10.5n + n2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -10.5n + -5.5 + n2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -10.5n + n2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -10.5n + n2 = 0 + -5.5 -10.5n + n2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -10.5n + n2 = -5.5 The n term is -10.5n. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5n + 27.5625 + n2 = -5.5 + 27.5625 Reorder the terms: 27.5625 + -10.5n + n2 = -5.5 + 27.5625 Combine like terms: -5.5 + 27.5625 = 22.0625 27.5625 + -10.5n + n2 = 22.0625 Factor a perfect square on the left side: (n + -5.25)(n + -5.25) = 22.0625 Calculate the square root of the right side: 4.697073557 Break this problem into two subproblems by setting (n + -5.25) equal to 4.697073557 and -4.697073557.Subproblem 1
n + -5.25 = 4.697073557 Simplifying n + -5.25 = 4.697073557 Reorder the terms: -5.25 + n = 4.697073557 Solving -5.25 + n = 4.697073557 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + n = 4.697073557 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + n = 4.697073557 + 5.25 n = 4.697073557 + 5.25 Combine like terms: 4.697073557 + 5.25 = 9.947073557 n = 9.947073557 Simplifying n = 9.947073557Subproblem 2
n + -5.25 = -4.697073557 Simplifying n + -5.25 = -4.697073557 Reorder the terms: -5.25 + n = -4.697073557 Solving -5.25 + n = -4.697073557 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + n = -4.697073557 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + n = -4.697073557 + 5.25 n = -4.697073557 + 5.25 Combine like terms: -4.697073557 + 5.25 = 0.552926443 n = 0.552926443 Simplifying n = 0.552926443Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.947073557, 0.552926443}
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