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Simplifying 36n2 + -72n = 360 Reorder the terms: -72n + 36n2 = 360 Solving -72n + 36n2 = 360 Solving for variable 'n'. Reorder the terms: -360 + -72n + 36n2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + -72n + 36n2 = 0 Factor out the Greatest Common Factor (GCF), '36'. 36(-10 + -2n + n2) = 0 Ignore the factor 36.Subproblem 1
Set the factor '(-10 + -2n + n2)' equal to zero and attempt to solve: Simplifying -10 + -2n + n2 = 0 Solving -10 + -2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -2n + 10 + n2 = 0 + 10 Reorder the terms: -10 + 10 + -2n + n2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -2n + n2 = 0 + 10 -2n + n2 = 0 + 10 Combine like terms: 0 + 10 = 10 -2n + n2 = 10 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = 10 + 1 Reorder the terms: 1 + -2n + n2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + -2n + n2 = 11 Factor a perfect square on the left side: (n + -1)(n + -1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (n + -1) equal to 3.31662479 and -3.31662479.Subproblem 1
n + -1 = 3.31662479 Simplifying n + -1 = 3.31662479 Reorder the terms: -1 + n = 3.31662479 Solving -1 + n = 3.31662479 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + n = 3.31662479 + 1 n = 3.31662479 + 1 Combine like terms: 3.31662479 + 1 = 4.31662479 n = 4.31662479 Simplifying n = 4.31662479Subproblem 2
n + -1 = -3.31662479 Simplifying n + -1 = -3.31662479 Reorder the terms: -1 + n = -3.31662479 Solving -1 + n = -3.31662479 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + n = -3.31662479 + 1 n = -3.31662479 + 1 Combine like terms: -3.31662479 + 1 = -2.31662479 n = -2.31662479 Simplifying n = -2.31662479Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.31662479, -2.31662479}Solution
n = {4.31662479, -2.31662479}
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