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Simplifying 4v2 = 5 + -11v Solving 4v2 = 5 + -11v Solving for variable 'v'. Reorder the terms: -5 + 11v + 4v2 = 5 + -11v + -5 + 11v Reorder the terms: -5 + 11v + 4v2 = 5 + -5 + -11v + 11v Combine like terms: 5 + -5 = 0 -5 + 11v + 4v2 = 0 + -11v + 11v -5 + 11v + 4v2 = -11v + 11v Combine like terms: -11v + 11v = 0 -5 + 11v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 2.75v + v2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 2.75v + 1.25 + v2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 2.75v + v2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 2.75v + v2 = 0 + 1.25 2.75v + v2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 2.75v + v2 = 1.25 The v term is 2.75v. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75v + 1.890625 + v2 = 1.25 + 1.890625 Reorder the terms: 1.890625 + 2.75v + v2 = 1.25 + 1.890625 Combine like terms: 1.25 + 1.890625 = 3.140625 1.890625 + 2.75v + v2 = 3.140625 Factor a perfect square on the left side: (v + 1.375)(v + 1.375) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (v + 1.375) equal to 1.77218086 and -1.77218086.Subproblem 1
v + 1.375 = 1.77218086 Simplifying v + 1.375 = 1.77218086 Reorder the terms: 1.375 + v = 1.77218086 Solving 1.375 + v = 1.77218086 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + v = 1.77218086 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + v = 1.77218086 + -1.375 v = 1.77218086 + -1.375 Combine like terms: 1.77218086 + -1.375 = 0.39718086 v = 0.39718086 Simplifying v = 0.39718086Subproblem 2
v + 1.375 = -1.77218086 Simplifying v + 1.375 = -1.77218086 Reorder the terms: 1.375 + v = -1.77218086 Solving 1.375 + v = -1.77218086 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + v = -1.77218086 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + v = -1.77218086 + -1.375 v = -1.77218086 + -1.375 Combine like terms: -1.77218086 + -1.375 = -3.14718086 v = -3.14718086 Simplifying v = -3.14718086Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.39718086, -3.14718086}
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