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Simplifying 2n2 + -21n + 7 = 0 Reorder the terms: 7 + -21n + 2n2 = 0 Solving 7 + -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'. 3.5 + -10.5n + n2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -10.5n + -3.5 + n2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -10.5n + n2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -10.5n + n2 = 0 + -3.5 -10.5n + n2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -10.5n + n2 = -3.5 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 = -3.5 + 27.5625 Reorder the terms: 27.5625 + -10.5n + n2 = -3.5 + 27.5625 Combine like terms: -3.5 + 27.5625 = 24.0625 27.5625 + -10.5n + n2 = 24.0625 Factor a perfect square on the left side: (n + -5.25)(n + -5.25) = 24.0625 Calculate the square root of the right side: 4.905354218 Break this problem into two subproblems by setting (n + -5.25) equal to 4.905354218 and -4.905354218.Subproblem 1
n + -5.25 = 4.905354218 Simplifying n + -5.25 = 4.905354218 Reorder the terms: -5.25 + n = 4.905354218 Solving -5.25 + n = 4.905354218 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 = 4.905354218 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + n = 4.905354218 + 5.25 n = 4.905354218 + 5.25 Combine like terms: 4.905354218 + 5.25 = 10.155354218 n = 10.155354218 Simplifying n = 10.155354218Subproblem 2
n + -5.25 = -4.905354218 Simplifying n + -5.25 = -4.905354218 Reorder the terms: -5.25 + n = -4.905354218 Solving -5.25 + n = -4.905354218 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 = -4.905354218 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + n = -4.905354218 + 5.25 n = -4.905354218 + 5.25 Combine like terms: -4.905354218 + 5.25 = 0.344645782 n = 0.344645782 Simplifying n = 0.344645782Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.155354218, 0.344645782}
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