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Simplifying 10v3 + -20v2 + -48v = 0 Reorder the terms: -48v + -20v2 + 10v3 = 0 Solving -48v + -20v2 + 10v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2v'. 2v(-24 + -10v + 5v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'v' equal to zero and attempt to solve: Simplifying v = 0 Solving v = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v = 0Subproblem 2
Set the factor '(-24 + -10v + 5v2)' equal to zero and attempt to solve: Simplifying -24 + -10v + 5v2 = 0 Solving -24 + -10v + 5v2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.8 + -2v + v2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + -2v + 4.8 + v2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + -2v + v2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + -2v + v2 = 0 + 4.8 -2v + v2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 -2v + v2 = 4.8 The v term is -2v. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2v + 1 + v2 = 4.8 + 1 Reorder the terms: 1 + -2v + v2 = 4.8 + 1 Combine like terms: 4.8 + 1 = 5.8 1 + -2v + v2 = 5.8 Factor a perfect square on the left side: (v + -1)(v + -1) = 5.8 Calculate the square root of the right side: 2.408318916 Break this problem into two subproblems by setting (v + -1) equal to 2.408318916 and -2.408318916.Subproblem 1
v + -1 = 2.408318916 Simplifying v + -1 = 2.408318916 Reorder the terms: -1 + v = 2.408318916 Solving -1 + v = 2.408318916 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = 2.408318916 + 1 Combine like terms: -1 + 1 = 0 0 + v = 2.408318916 + 1 v = 2.408318916 + 1 Combine like terms: 2.408318916 + 1 = 3.408318916 v = 3.408318916 Simplifying v = 3.408318916Subproblem 2
v + -1 = -2.408318916 Simplifying v + -1 = -2.408318916 Reorder the terms: -1 + v = -2.408318916 Solving -1 + v = -2.408318916 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + v = -2.408318916 + 1 Combine like terms: -1 + 1 = 0 0 + v = -2.408318916 + 1 v = -2.408318916 + 1 Combine like terms: -2.408318916 + 1 = -1.408318916 v = -1.408318916 Simplifying v = -1.408318916Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.408318916, -1.408318916}Solution
v = {0, 3.408318916, -1.408318916}
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