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Simplifying 2v2 + 3v = 4 Reorder the terms: 3v + 2v2 = 4 Solving 3v + 2v2 = 4 Solving for variable 'v'. Reorder the terms: -4 + 3v + 2v2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 3v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + 1.5v + v2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.5v + 2 + v2 = 0 + 2 Reorder the terms: -2 + 2 + 1.5v + v2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.5v + v2 = 0 + 2 1.5v + v2 = 0 + 2 Combine like terms: 0 + 2 = 2 1.5v + v2 = 2 The v term is 1.5v. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5v + 0.5625 + v2 = 2 + 0.5625 Reorder the terms: 0.5625 + 1.5v + v2 = 2 + 0.5625 Combine like terms: 2 + 0.5625 = 2.5625 0.5625 + 1.5v + v2 = 2.5625 Factor a perfect square on the left side: (v + 0.75)(v + 0.75) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (v + 0.75) equal to 1.600781059 and -1.600781059.Subproblem 1
v + 0.75 = 1.600781059 Simplifying v + 0.75 = 1.600781059 Reorder the terms: 0.75 + v = 1.600781059 Solving 0.75 + v = 1.600781059 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + v = 1.600781059 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + v = 1.600781059 + -0.75 v = 1.600781059 + -0.75 Combine like terms: 1.600781059 + -0.75 = 0.850781059 v = 0.850781059 Simplifying v = 0.850781059Subproblem 2
v + 0.75 = -1.600781059 Simplifying v + 0.75 = -1.600781059 Reorder the terms: 0.75 + v = -1.600781059 Solving 0.75 + v = -1.600781059 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + v = -1.600781059 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + v = -1.600781059 + -0.75 v = -1.600781059 + -0.75 Combine like terms: -1.600781059 + -0.75 = -2.350781059 v = -2.350781059 Simplifying v = -2.350781059Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.850781059, -2.350781059}
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