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Simplifying 6v2 + -27v + 18 = 0 Reorder the terms: 18 + -27v + 6v2 = 0 Solving 18 + -27v + 6v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '3'. 3(6 + -9v + 2v2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + -9v + 2v2)' equal to zero and attempt to solve: Simplifying 6 + -9v + 2v2 = 0 Solving 6 + -9v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + -4.5v + v2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -4.5v + -3 + v2 = 0 + -3 Reorder the terms: 3 + -3 + -4.5v + v2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4.5v + v2 = 0 + -3 -4.5v + v2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4.5v + v2 = -3 The v term is -4.5v. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5v + 5.0625 + v2 = -3 + 5.0625 Reorder the terms: 5.0625 + -4.5v + v2 = -3 + 5.0625 Combine like terms: -3 + 5.0625 = 2.0625 5.0625 + -4.5v + v2 = 2.0625 Factor a perfect square on the left side: (v + -2.25)(v + -2.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (v + -2.25) equal to 1.436140662 and -1.436140662.Subproblem 1
v + -2.25 = 1.436140662 Simplifying v + -2.25 = 1.436140662 Reorder the terms: -2.25 + v = 1.436140662 Solving -2.25 + v = 1.436140662 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + v = 1.436140662 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + v = 1.436140662 + 2.25 v = 1.436140662 + 2.25 Combine like terms: 1.436140662 + 2.25 = 3.686140662 v = 3.686140662 Simplifying v = 3.686140662Subproblem 2
v + -2.25 = -1.436140662 Simplifying v + -2.25 = -1.436140662 Reorder the terms: -2.25 + v = -1.436140662 Solving -2.25 + v = -1.436140662 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + v = -1.436140662 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + v = -1.436140662 + 2.25 v = -1.436140662 + 2.25 Combine like terms: -1.436140662 + 2.25 = 0.813859338 v = 0.813859338 Simplifying v = 0.813859338Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.686140662, 0.813859338}Solution
v = {3.686140662, 0.813859338}
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