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Simplifying 4n2 + -1n + -2 = 0 Reorder the terms: -2 + -1n + 4n2 = 0 Solving -2 + -1n + 4n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.5 + -0.25n + n2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.25n + 0.5 + n2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.25n + n2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.25n + n2 = 0 + 0.5 -0.25n + n2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.25n + n2 = 0.5 The n term is -0.25n. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25n + 0.015625 + n2 = 0.5 + 0.015625 Reorder the terms: 0.015625 + -0.25n + n2 = 0.5 + 0.015625 Combine like terms: 0.5 + 0.015625 = 0.515625 0.015625 + -0.25n + n2 = 0.515625 Factor a perfect square on the left side: (n + -0.125)(n + -0.125) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (n + -0.125) equal to 0.718070331 and -0.718070331.Subproblem 1
n + -0.125 = 0.718070331 Simplifying n + -0.125 = 0.718070331 Reorder the terms: -0.125 + n = 0.718070331 Solving -0.125 + n = 0.718070331 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + n = 0.718070331 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + n = 0.718070331 + 0.125 n = 0.718070331 + 0.125 Combine like terms: 0.718070331 + 0.125 = 0.843070331 n = 0.843070331 Simplifying n = 0.843070331Subproblem 2
n + -0.125 = -0.718070331 Simplifying n + -0.125 = -0.718070331 Reorder the terms: -0.125 + n = -0.718070331 Solving -0.125 + n = -0.718070331 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + n = -0.718070331 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + n = -0.718070331 + 0.125 n = -0.718070331 + 0.125 Combine like terms: -0.718070331 + 0.125 = -0.593070331 n = -0.593070331 Simplifying n = -0.593070331Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.843070331, -0.593070331}
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