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Simplifying 17n2 + 19n = 6 Reorder the terms: 19n + 17n2 = 6 Solving 19n + 17n2 = 6 Solving for variable 'n'. Reorder the terms: -6 + 19n + 17n2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 19n + 17n2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.3529411765 + 1.117647059n + n2 = 0 Move the constant term to the right: Add '0.3529411765' to each side of the equation. -0.3529411765 + 1.117647059n + 0.3529411765 + n2 = 0 + 0.3529411765 Reorder the terms: -0.3529411765 + 0.3529411765 + 1.117647059n + n2 = 0 + 0.3529411765 Combine like terms: -0.3529411765 + 0.3529411765 = 0.0000000000 0.0000000000 + 1.117647059n + n2 = 0 + 0.3529411765 1.117647059n + n2 = 0 + 0.3529411765 Combine like terms: 0 + 0.3529411765 = 0.3529411765 1.117647059n + n2 = 0.3529411765 The n term is 1.117647059n. Take half its coefficient (0.5588235295). Square it (0.3122837371) and add it to both sides. Add '0.3122837371' to each side of the equation. 1.117647059n + 0.3122837371 + n2 = 0.3529411765 + 0.3122837371 Reorder the terms: 0.3122837371 + 1.117647059n + n2 = 0.3529411765 + 0.3122837371 Combine like terms: 0.3529411765 + 0.3122837371 = 0.6652249136 0.3122837371 + 1.117647059n + n2 = 0.6652249136 Factor a perfect square on the left side: (n + 0.5588235295)(n + 0.5588235295) = 0.6652249136 Calculate the square root of the right side: 0.815613213 Break this problem into two subproblems by setting (n + 0.5588235295) equal to 0.815613213 and -0.815613213.Subproblem 1
n + 0.5588235295 = 0.815613213 Simplifying n + 0.5588235295 = 0.815613213 Reorder the terms: 0.5588235295 + n = 0.815613213 Solving 0.5588235295 + n = 0.815613213 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5588235295' to each side of the equation. 0.5588235295 + -0.5588235295 + n = 0.815613213 + -0.5588235295 Combine like terms: 0.5588235295 + -0.5588235295 = 0.0000000000 0.0000000000 + n = 0.815613213 + -0.5588235295 n = 0.815613213 + -0.5588235295 Combine like terms: 0.815613213 + -0.5588235295 = 0.2567896835 n = 0.2567896835 Simplifying n = 0.2567896835Subproblem 2
n + 0.5588235295 = -0.815613213 Simplifying n + 0.5588235295 = -0.815613213 Reorder the terms: 0.5588235295 + n = -0.815613213 Solving 0.5588235295 + n = -0.815613213 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5588235295' to each side of the equation. 0.5588235295 + -0.5588235295 + n = -0.815613213 + -0.5588235295 Combine like terms: 0.5588235295 + -0.5588235295 = 0.0000000000 0.0000000000 + n = -0.815613213 + -0.5588235295 n = -0.815613213 + -0.5588235295 Combine like terms: -0.815613213 + -0.5588235295 = -1.3744367425 n = -1.3744367425 Simplifying n = -1.3744367425Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.2567896835, -1.3744367425}
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