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Simplifying 2n3 + -18n2 + -14n = 0 Reorder the terms: -14n + -18n2 + 2n3 = 0 Solving -14n + -18n2 + 2n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2n'. 2n(-7 + -9n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(-7 + -9n + n2)' equal to zero and attempt to solve: Simplifying -7 + -9n + n2 = 0 Solving -7 + -9n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -9n + 7 + n2 = 0 + 7 Reorder the terms: -7 + 7 + -9n + n2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -9n + n2 = 0 + 7 -9n + n2 = 0 + 7 Combine like terms: 0 + 7 = 7 -9n + n2 = 7 The n term is -9n. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9n + 20.25 + n2 = 7 + 20.25 Reorder the terms: 20.25 + -9n + n2 = 7 + 20.25 Combine like terms: 7 + 20.25 = 27.25 20.25 + -9n + n2 = 27.25 Factor a perfect square on the left side: (n + -4.5)(n + -4.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (n + -4.5) equal to 5.220153254 and -5.220153254.Subproblem 1
n + -4.5 = 5.220153254 Simplifying n + -4.5 = 5.220153254 Reorder the terms: -4.5 + n = 5.220153254 Solving -4.5 + n = 5.220153254 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = 5.220153254 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = 5.220153254 + 4.5 n = 5.220153254 + 4.5 Combine like terms: 5.220153254 + 4.5 = 9.720153254 n = 9.720153254 Simplifying n = 9.720153254Subproblem 2
n + -4.5 = -5.220153254 Simplifying n + -4.5 = -5.220153254 Reorder the terms: -4.5 + n = -5.220153254 Solving -4.5 + n = -5.220153254 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = -5.220153254 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = -5.220153254 + 4.5 n = -5.220153254 + 4.5 Combine like terms: -5.220153254 + 4.5 = -0.720153254 n = -0.720153254 Simplifying n = -0.720153254Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.720153254, -0.720153254}Solution
n = {0, 9.720153254, -0.720153254}
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