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Simplifying v3 + 4v2 + -4v = 0 Reorder the terms: -4v + 4v2 + v3 = 0 Solving -4v + 4v2 + v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), 'v'. v(-4 + 4v + v2) = 0Subproblem 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 '(-4 + 4v + v2)' equal to zero and attempt to solve: Simplifying -4 + 4v + v2 = 0 Solving -4 + 4v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 4v + 4 + v2 = 0 + 4 Reorder the terms: -4 + 4 + 4v + v2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4v + v2 = 0 + 4 4v + v2 = 0 + 4 Combine like terms: 0 + 4 = 4 4v + v2 = 4 The v term is 4v. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4v + 4 + v2 = 4 + 4 Reorder the terms: 4 + 4v + v2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + 4v + v2 = 8 Factor a perfect square on the left side: (v + 2)(v + 2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (v + 2) equal to 2.828427125 and -2.828427125.Subproblem 1
v + 2 = 2.828427125 Simplifying v + 2 = 2.828427125 Reorder the terms: 2 + v = 2.828427125 Solving 2 + v = 2.828427125 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = 2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + v = 2.828427125 + -2 v = 2.828427125 + -2 Combine like terms: 2.828427125 + -2 = 0.828427125 v = 0.828427125 Simplifying v = 0.828427125Subproblem 2
v + 2 = -2.828427125 Simplifying v + 2 = -2.828427125 Reorder the terms: 2 + v = -2.828427125 Solving 2 + v = -2.828427125 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = -2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + v = -2.828427125 + -2 v = -2.828427125 + -2 Combine like terms: -2.828427125 + -2 = -4.828427125 v = -4.828427125 Simplifying v = -4.828427125Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.828427125, -4.828427125}Solution
v = {0, 0.828427125, -4.828427125}
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