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Simplifying 4n2 = 13 + 4n Solving 4n2 = 13 + 4n Solving for variable 'n'. Reorder the terms: -13 + -4n + 4n2 = 13 + 4n + -13 + -4n Reorder the terms: -13 + -4n + 4n2 = 13 + -13 + 4n + -4n Combine like terms: 13 + -13 = 0 -13 + -4n + 4n2 = 0 + 4n + -4n -13 + -4n + 4n2 = 4n + -4n Combine like terms: 4n + -4n = 0 -13 + -4n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + -1n + n2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + -1n + 3.25 + n2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + -1n + n2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + -1n + n2 = 0 + 3.25 -1n + n2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 -1n + n2 = 3.25 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 = 3.25 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 3.25 + 0.25 Combine like terms: 3.25 + 0.25 = 3.5 0.25 + -1n + n2 = 3.5 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (n + -0.5) equal to 1.870828693 and -1.870828693.Subproblem 1
n + -0.5 = 1.870828693 Simplifying n + -0.5 = 1.870828693 Reorder the terms: -0.5 + n = 1.870828693 Solving -0.5 + n = 1.870828693 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 = 1.870828693 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 1.870828693 + 0.5 n = 1.870828693 + 0.5 Combine like terms: 1.870828693 + 0.5 = 2.370828693 n = 2.370828693 Simplifying n = 2.370828693Subproblem 2
n + -0.5 = -1.870828693 Simplifying n + -0.5 = -1.870828693 Reorder the terms: -0.5 + n = -1.870828693 Solving -0.5 + n = -1.870828693 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 = -1.870828693 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -1.870828693 + 0.5 n = -1.870828693 + 0.5 Combine like terms: -1.870828693 + 0.5 = -1.370828693 n = -1.370828693 Simplifying n = -1.370828693Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.370828693, -1.370828693}
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