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Simplifying 5n2 = -5n + 160 Reorder the terms: 5n2 = 160 + -5n Solving 5n2 = 160 + -5n Solving for variable 'n'. Reorder the terms: -160 + 5n + 5n2 = 160 + -5n + -160 + 5n Reorder the terms: -160 + 5n + 5n2 = 160 + -160 + -5n + 5n Combine like terms: 160 + -160 = 0 -160 + 5n + 5n2 = 0 + -5n + 5n -160 + 5n + 5n2 = -5n + 5n Combine like terms: -5n + 5n = 0 -160 + 5n + 5n2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-32 + n + n2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-32 + n + n2)' equal to zero and attempt to solve: Simplifying -32 + n + n2 = 0 Solving -32 + n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + n + 32 + n2 = 0 + 32 Reorder the terms: -32 + 32 + n + n2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + n + n2 = 0 + 32 n + n2 = 0 + 32 Combine like terms: 0 + 32 = 32 n + n2 = 32 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. n + 0.25 + n2 = 32 + 0.25 Reorder the terms: 0.25 + n + n2 = 32 + 0.25 Combine like terms: 32 + 0.25 = 32.25 0.25 + n + n2 = 32.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (n + 0.5) equal to 5.678908346 and -5.678908346.Subproblem 1
n + 0.5 = 5.678908346 Simplifying n + 0.5 = 5.678908346 Reorder the terms: 0.5 + n = 5.678908346 Solving 0.5 + n = 5.678908346 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 5.678908346 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 5.678908346 + -0.5 n = 5.678908346 + -0.5 Combine like terms: 5.678908346 + -0.5 = 5.178908346 n = 5.178908346 Simplifying n = 5.178908346Subproblem 2
n + 0.5 = -5.678908346 Simplifying n + 0.5 = -5.678908346 Reorder the terms: 0.5 + n = -5.678908346 Solving 0.5 + n = -5.678908346 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -5.678908346 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -5.678908346 + -0.5 n = -5.678908346 + -0.5 Combine like terms: -5.678908346 + -0.5 = -6.178908346 n = -6.178908346 Simplifying n = -6.178908346Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.178908346, -6.178908346}Solution
n = {5.178908346, -6.178908346}
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