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Simplifying 4n2 + -12n + -320 = 0 Reorder the terms: -320 + -12n + 4n2 = 0 Solving -320 + -12n + 4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(-80 + -3n + n2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-80 + -3n + n2)' equal to zero and attempt to solve: Simplifying -80 + -3n + n2 = 0 Solving -80 + -3n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -3n + 80 + n2 = 0 + 80 Reorder the terms: -80 + 80 + -3n + n2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -3n + n2 = 0 + 80 -3n + n2 = 0 + 80 Combine like terms: 0 + 80 = 80 -3n + n2 = 80 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 80 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 80 + 2.25 Combine like terms: 80 + 2.25 = 82.25 2.25 + -3n + n2 = 82.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (n + -1.5) equal to 9.069178574 and -9.069178574.Subproblem 1
n + -1.5 = 9.069178574 Simplifying n + -1.5 = 9.069178574 Reorder the terms: -1.5 + n = 9.069178574 Solving -1.5 + n = 9.069178574 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 9.069178574 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 9.069178574 + 1.5 n = 9.069178574 + 1.5 Combine like terms: 9.069178574 + 1.5 = 10.569178574 n = 10.569178574 Simplifying n = 10.569178574Subproblem 2
n + -1.5 = -9.069178574 Simplifying n + -1.5 = -9.069178574 Reorder the terms: -1.5 + n = -9.069178574 Solving -1.5 + n = -9.069178574 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -9.069178574 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -9.069178574 + 1.5 n = -9.069178574 + 1.5 Combine like terms: -9.069178574 + 1.5 = -7.569178574 n = -7.569178574 Simplifying n = -7.569178574Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.569178574, -7.569178574}Solution
n = {10.569178574, -7.569178574}
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