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Simplifying 2n2 + -10n + -8 = 0 Reorder the terms: -8 + -10n + 2n2 = 0 Solving -8 + -10n + 2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -5n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -5n + n2)' equal to zero and attempt to solve: Simplifying -4 + -5n + n2 = 0 Solving -4 + -5n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -5n + 4 + n2 = 0 + 4 Reorder the terms: -4 + 4 + -5n + n2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5n + n2 = 0 + 4 -5n + n2 = 0 + 4 Combine like terms: 0 + 4 = 4 -5n + n2 = 4 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 = 4 + 6.25 Reorder the terms: 6.25 + -5n + n2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + -5n + n2 = 10.25 Factor a perfect square on the left side: (n + -2.5)(n + -2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (n + -2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
n + -2.5 = 3.201562119 Simplifying n + -2.5 = 3.201562119 Reorder the terms: -2.5 + n = 3.201562119 Solving -2.5 + n = 3.201562119 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 = 3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = 3.201562119 + 2.5 n = 3.201562119 + 2.5 Combine like terms: 3.201562119 + 2.5 = 5.701562119 n = 5.701562119 Simplifying n = 5.701562119Subproblem 2
n + -2.5 = -3.201562119 Simplifying n + -2.5 = -3.201562119 Reorder the terms: -2.5 + n = -3.201562119 Solving -2.5 + n = -3.201562119 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 = -3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = -3.201562119 + 2.5 n = -3.201562119 + 2.5 Combine like terms: -3.201562119 + 2.5 = -0.701562119 n = -0.701562119 Simplifying n = -0.701562119Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.701562119, -0.701562119}Solution
n = {5.701562119, -0.701562119}
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