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Simplifying 72v2 + -42 = -35v Reorder the terms: -42 + 72v2 = -35v Solving -42 + 72v2 = -35v Solving for variable 'v'. Reorder the terms: -42 + 35v + 72v2 = -35v + 35v Combine like terms: -35v + 35v = 0 -42 + 35v + 72v2 = 0 Begin completing the square. Divide all terms by 72 the coefficient of the squared term: Divide each side by '72'. -0.5833333333 + 0.4861111111v + v2 = 0 Move the constant term to the right: Add '0.5833333333' to each side of the equation. -0.5833333333 + 0.4861111111v + 0.5833333333 + v2 = 0 + 0.5833333333 Reorder the terms: -0.5833333333 + 0.5833333333 + 0.4861111111v + v2 = 0 + 0.5833333333 Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000 0.0000000000 + 0.4861111111v + v2 = 0 + 0.5833333333 0.4861111111v + v2 = 0 + 0.5833333333 Combine like terms: 0 + 0.5833333333 = 0.5833333333 0.4861111111v + v2 = 0.5833333333 The v term is 0.4861111111v. Take half its coefficient (0.2430555556). Square it (0.05907600311) and add it to both sides. Add '0.05907600311' to each side of the equation. 0.4861111111v + 0.05907600311 + v2 = 0.5833333333 + 0.05907600311 Reorder the terms: 0.05907600311 + 0.4861111111v + v2 = 0.5833333333 + 0.05907600311 Combine like terms: 0.5833333333 + 0.05907600311 = 0.64240933641 0.05907600311 + 0.4861111111v + v2 = 0.64240933641 Factor a perfect square on the left side: (v + 0.2430555556)(v + 0.2430555556) = 0.64240933641 Calculate the square root of the right side: 0.801504421 Break this problem into two subproblems by setting (v + 0.2430555556) equal to 0.801504421 and -0.801504421.Subproblem 1
v + 0.2430555556 = 0.801504421 Simplifying v + 0.2430555556 = 0.801504421 Reorder the terms: 0.2430555556 + v = 0.801504421 Solving 0.2430555556 + v = 0.801504421 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.2430555556' to each side of the equation. 0.2430555556 + -0.2430555556 + v = 0.801504421 + -0.2430555556 Combine like terms: 0.2430555556 + -0.2430555556 = 0.0000000000 0.0000000000 + v = 0.801504421 + -0.2430555556 v = 0.801504421 + -0.2430555556 Combine like terms: 0.801504421 + -0.2430555556 = 0.5584488654 v = 0.5584488654 Simplifying v = 0.5584488654Subproblem 2
v + 0.2430555556 = -0.801504421 Simplifying v + 0.2430555556 = -0.801504421 Reorder the terms: 0.2430555556 + v = -0.801504421 Solving 0.2430555556 + v = -0.801504421 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.2430555556' to each side of the equation. 0.2430555556 + -0.2430555556 + v = -0.801504421 + -0.2430555556 Combine like terms: 0.2430555556 + -0.2430555556 = 0.0000000000 0.0000000000 + v = -0.801504421 + -0.2430555556 v = -0.801504421 + -0.2430555556 Combine like terms: -0.801504421 + -0.2430555556 = -1.0445599766 v = -1.0445599766 Simplifying v = -1.0445599766Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.5584488654, -1.0445599766}
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