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Simplifying 20n2 + -16n + -160 = 0 Reorder the terms: -160 + -16n + 20n2 = 0 Solving -160 + -16n + 20n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(-40 + -4n + 5n2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-40 + -4n + 5n2)' equal to zero and attempt to solve: Simplifying -40 + -4n + 5n2 = 0 Solving -40 + -4n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8 + -0.8n + n2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -0.8n + 8 + n2 = 0 + 8 Reorder the terms: -8 + 8 + -0.8n + n2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -0.8n + n2 = 0 + 8 -0.8n + n2 = 0 + 8 Combine like terms: 0 + 8 = 8 -0.8n + n2 = 8 The n term is -0.8n. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8n + 0.16 + n2 = 8 + 0.16 Reorder the terms: 0.16 + -0.8n + n2 = 8 + 0.16 Combine like terms: 8 + 0.16 = 8.16 0.16 + -0.8n + n2 = 8.16 Factor a perfect square on the left side: (n + -0.4)(n + -0.4) = 8.16 Calculate the square root of the right side: 2.856571371 Break this problem into two subproblems by setting (n + -0.4) equal to 2.856571371 and -2.856571371.Subproblem 1
n + -0.4 = 2.856571371 Simplifying n + -0.4 = 2.856571371 Reorder the terms: -0.4 + n = 2.856571371 Solving -0.4 + n = 2.856571371 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + n = 2.856571371 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + n = 2.856571371 + 0.4 n = 2.856571371 + 0.4 Combine like terms: 2.856571371 + 0.4 = 3.256571371 n = 3.256571371 Simplifying n = 3.256571371Subproblem 2
n + -0.4 = -2.856571371 Simplifying n + -0.4 = -2.856571371 Reorder the terms: -0.4 + n = -2.856571371 Solving -0.4 + n = -2.856571371 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + n = -2.856571371 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + n = -2.856571371 + 0.4 n = -2.856571371 + 0.4 Combine like terms: -2.856571371 + 0.4 = -2.456571371 n = -2.456571371 Simplifying n = -2.456571371Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.256571371, -2.456571371}Solution
n = {3.256571371, -2.456571371}
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