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Simplifying n2 + -5n + 3 = 0 Reorder the terms: 3 + -5n + n2 = 0 Solving 3 + -5n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -5n + -3 + n2 = 0 + -3 Reorder the terms: 3 + -3 + -5n + n2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5n + n2 = 0 + -3 -5n + n2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5n + n2 = -3 The n term is -5n. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5n + 6.25 + n2 = -3 + 6.25 Reorder the terms: 6.25 + -5n + n2 = -3 + 6.25 Combine like terms: -3 + 6.25 = 3.25 6.25 + -5n + n2 = 3.25 Factor a perfect square on the left side: (n + -2.5)(n + -2.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (n + -2.5) equal to 1.802775638 and -1.802775638.Subproblem 1
n + -2.5 = 1.802775638 Simplifying n + -2.5 = 1.802775638 Reorder the terms: -2.5 + n = 1.802775638 Solving -2.5 + n = 1.802775638 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = 1.802775638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = 1.802775638 + 2.5 n = 1.802775638 + 2.5 Combine like terms: 1.802775638 + 2.5 = 4.302775638 n = 4.302775638 Simplifying n = 4.302775638Subproblem 2
n + -2.5 = -1.802775638 Simplifying n + -2.5 = -1.802775638 Reorder the terms: -2.5 + n = -1.802775638 Solving -2.5 + n = -1.802775638 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = -1.802775638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = -1.802775638 + 2.5 n = -1.802775638 + 2.5 Combine like terms: -1.802775638 + 2.5 = 0.697224362 n = 0.697224362 Simplifying n = 0.697224362Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.302775638, 0.697224362}
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