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Simplifying 6v2 + 12v + -62 = 0 Reorder the terms: -62 + 12v + 6v2 = 0 Solving -62 + 12v + 6v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-31 + 6v + 3v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-31 + 6v + 3v2)' equal to zero and attempt to solve: Simplifying -31 + 6v + 3v2 = 0 Solving -31 + 6v + 3v2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10.33333333 + 2v + v2 = 0 Move the constant term to the right: Add '10.33333333' to each side of the equation. -10.33333333 + 2v + 10.33333333 + v2 = 0 + 10.33333333 Reorder the terms: -10.33333333 + 10.33333333 + 2v + v2 = 0 + 10.33333333 Combine like terms: -10.33333333 + 10.33333333 = 0.00000000 0.00000000 + 2v + v2 = 0 + 10.33333333 2v + v2 = 0 + 10.33333333 Combine like terms: 0 + 10.33333333 = 10.33333333 2v + v2 = 10.33333333 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 = 10.33333333 + 1 Reorder the terms: 1 + 2v + v2 = 10.33333333 + 1 Combine like terms: 10.33333333 + 1 = 11.33333333 1 + 2v + v2 = 11.33333333 Factor a perfect square on the left side: (v + 1)(v + 1) = 11.33333333 Calculate the square root of the right side: 3.366501646 Break this problem into two subproblems by setting (v + 1) equal to 3.366501646 and -3.366501646.Subproblem 1
v + 1 = 3.366501646 Simplifying v + 1 = 3.366501646 Reorder the terms: 1 + v = 3.366501646 Solving 1 + v = 3.366501646 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 = 3.366501646 + -1 Combine like terms: 1 + -1 = 0 0 + v = 3.366501646 + -1 v = 3.366501646 + -1 Combine like terms: 3.366501646 + -1 = 2.366501646 v = 2.366501646 Simplifying v = 2.366501646Subproblem 2
v + 1 = -3.366501646 Simplifying v + 1 = -3.366501646 Reorder the terms: 1 + v = -3.366501646 Solving 1 + v = -3.366501646 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 = -3.366501646 + -1 Combine like terms: 1 + -1 = 0 0 + v = -3.366501646 + -1 v = -3.366501646 + -1 Combine like terms: -3.366501646 + -1 = -4.366501646 v = -4.366501646 Simplifying v = -4.366501646Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.366501646, -4.366501646}Solution
v = {2.366501646, -4.366501646}
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