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Simplifying 8v2 + 16v + -44 = 0 Reorder the terms: -44 + 16v + 8v2 = 0 Solving -44 + 16v + 8v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '4'. 4(-11 + 4v + 2v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-11 + 4v + 2v2)' equal to zero and attempt to solve: Simplifying -11 + 4v + 2v2 = 0 Solving -11 + 4v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + 2v + v2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 2v + 5.5 + v2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 2v + v2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 2v + v2 = 0 + 5.5 2v + v2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 2v + v2 = 5.5 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 = 5.5 + 1 Reorder the terms: 1 + 2v + v2 = 5.5 + 1 Combine like terms: 5.5 + 1 = 6.5 1 + 2v + v2 = 6.5 Factor a perfect square on the left side: (v + 1)(v + 1) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (v + 1) equal to 2.549509757 and -2.549509757.Subproblem 1
v + 1 = 2.549509757 Simplifying v + 1 = 2.549509757 Reorder the terms: 1 + v = 2.549509757 Solving 1 + v = 2.549509757 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 = 2.549509757 + -1 Combine like terms: 1 + -1 = 0 0 + v = 2.549509757 + -1 v = 2.549509757 + -1 Combine like terms: 2.549509757 + -1 = 1.549509757 v = 1.549509757 Simplifying v = 1.549509757Subproblem 2
v + 1 = -2.549509757 Simplifying v + 1 = -2.549509757 Reorder the terms: 1 + v = -2.549509757 Solving 1 + v = -2.549509757 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 = -2.549509757 + -1 Combine like terms: 1 + -1 = 0 0 + v = -2.549509757 + -1 v = -2.549509757 + -1 Combine like terms: -2.549509757 + -1 = -3.549509757 v = -3.549509757 Simplifying v = -3.549509757Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.549509757, -3.549509757}Solution
v = {1.549509757, -3.549509757}
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