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Simplifying n2 + -12n + 25 = 0 Reorder the terms: 25 + -12n + n2 = 0 Solving 25 + -12n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -12n + -25 + n2 = 0 + -25 Reorder the terms: 25 + -25 + -12n + n2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -12n + n2 = 0 + -25 -12n + n2 = 0 + -25 Combine like terms: 0 + -25 = -25 -12n + n2 = -25 The n term is -12n. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12n + 36 + n2 = -25 + 36 Reorder the terms: 36 + -12n + n2 = -25 + 36 Combine like terms: -25 + 36 = 11 36 + -12n + n2 = 11 Factor a perfect square on the left side: (n + -6)(n + -6) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (n + -6) equal to 3.31662479 and -3.31662479.Subproblem 1
n + -6 = 3.31662479 Simplifying n + -6 = 3.31662479 Reorder the terms: -6 + n = 3.31662479 Solving -6 + n = 3.31662479 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = 3.31662479 + 6 Combine like terms: -6 + 6 = 0 0 + n = 3.31662479 + 6 n = 3.31662479 + 6 Combine like terms: 3.31662479 + 6 = 9.31662479 n = 9.31662479 Simplifying n = 9.31662479Subproblem 2
n + -6 = -3.31662479 Simplifying n + -6 = -3.31662479 Reorder the terms: -6 + n = -3.31662479 Solving -6 + n = -3.31662479 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = -3.31662479 + 6 Combine like terms: -6 + 6 = 0 0 + n = -3.31662479 + 6 n = -3.31662479 + 6 Combine like terms: -3.31662479 + 6 = 2.68337521 n = 2.68337521 Simplifying n = 2.68337521Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.31662479, 2.68337521}
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