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Simplifying 8n2 + -57n + 2 = 0 Reorder the terms: 2 + -57n + 8n2 = 0 Solving 2 + -57n + 8n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.25 + -7.125n + n2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -7.125n + -0.25 + n2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -7.125n + n2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -7.125n + n2 = 0 + -0.25 -7.125n + n2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -7.125n + n2 = -0.25 The n term is -7.125n. Take half its coefficient (-3.5625). Square it (12.69140625) and add it to both sides. Add '12.69140625' to each side of the equation. -7.125n + 12.69140625 + n2 = -0.25 + 12.69140625 Reorder the terms: 12.69140625 + -7.125n + n2 = -0.25 + 12.69140625 Combine like terms: -0.25 + 12.69140625 = 12.44140625 12.69140625 + -7.125n + n2 = 12.44140625 Factor a perfect square on the left side: (n + -3.5625)(n + -3.5625) = 12.44140625 Calculate the square root of the right side: 3.527237765 Break this problem into two subproblems by setting (n + -3.5625) equal to 3.527237765 and -3.527237765.Subproblem 1
n + -3.5625 = 3.527237765 Simplifying n + -3.5625 = 3.527237765 Reorder the terms: -3.5625 + n = 3.527237765 Solving -3.5625 + n = 3.527237765 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.5625' to each side of the equation. -3.5625 + 3.5625 + n = 3.527237765 + 3.5625 Combine like terms: -3.5625 + 3.5625 = 0.0000 0.0000 + n = 3.527237765 + 3.5625 n = 3.527237765 + 3.5625 Combine like terms: 3.527237765 + 3.5625 = 7.089737765 n = 7.089737765 Simplifying n = 7.089737765Subproblem 2
n + -3.5625 = -3.527237765 Simplifying n + -3.5625 = -3.527237765 Reorder the terms: -3.5625 + n = -3.527237765 Solving -3.5625 + n = -3.527237765 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.5625' to each side of the equation. -3.5625 + 3.5625 + n = -3.527237765 + 3.5625 Combine like terms: -3.5625 + 3.5625 = 0.0000 0.0000 + n = -3.527237765 + 3.5625 n = -3.527237765 + 3.5625 Combine like terms: -3.527237765 + 3.5625 = 0.035262235 n = 0.035262235 Simplifying n = 0.035262235Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.089737765, 0.035262235}
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