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Simplifying 6v3 + -21v2 + 9v = 3v Reorder the terms: 9v + -21v2 + 6v3 = 3v Solving 9v + -21v2 + 6v3 = 3v Solving for variable 'v'. Reorder the terms: 9v + -3v + -21v2 + 6v3 = 3v + -3v Combine like terms: 9v + -3v = 6v 6v + -21v2 + 6v3 = 3v + -3v Combine like terms: 3v + -3v = 0 6v + -21v2 + 6v3 = 0 Factor out the Greatest Common Factor (GCF), '3v'. 3v(2 + -7v + 2v2) = 0 Ignore the factor 3.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 '(2 + -7v + 2v2)' equal to zero and attempt to solve: Simplifying 2 + -7v + 2v2 = 0 Solving 2 + -7v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + -3.5v + v2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -3.5v + -1 + v2 = 0 + -1 Reorder the terms: 1 + -1 + -3.5v + v2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3.5v + v2 = 0 + -1 -3.5v + v2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3.5v + v2 = -1 The v term is -3.5v. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5v + 3.0625 + v2 = -1 + 3.0625 Reorder the terms: 3.0625 + -3.5v + v2 = -1 + 3.0625 Combine like terms: -1 + 3.0625 = 2.0625 3.0625 + -3.5v + v2 = 2.0625 Factor a perfect square on the left side: (v + -1.75)(v + -1.75) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (v + -1.75) equal to 1.436140662 and -1.436140662.Subproblem 1
v + -1.75 = 1.436140662 Simplifying v + -1.75 = 1.436140662 Reorder the terms: -1.75 + v = 1.436140662 Solving -1.75 + v = 1.436140662 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + v = 1.436140662 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + v = 1.436140662 + 1.75 v = 1.436140662 + 1.75 Combine like terms: 1.436140662 + 1.75 = 3.186140662 v = 3.186140662 Simplifying v = 3.186140662Subproblem 2
v + -1.75 = -1.436140662 Simplifying v + -1.75 = -1.436140662 Reorder the terms: -1.75 + v = -1.436140662 Solving -1.75 + v = -1.436140662 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + v = -1.436140662 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + v = -1.436140662 + 1.75 v = -1.436140662 + 1.75 Combine like terms: -1.436140662 + 1.75 = 0.313859338 v = 0.313859338 Simplifying v = 0.313859338Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.186140662, 0.313859338}Solution
v = {0, 3.186140662, 0.313859338}
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