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Simplifying 0.04v2 + 0.5v = 67 Reorder the terms: 0.5v + 0.04v2 = 67 Solving 0.5v + 0.04v2 = 67 Solving for variable 'v'. Reorder the terms: -67 + 0.5v + 0.04v2 = 67 + -67 Combine like terms: 67 + -67 = 0 -67 + 0.5v + 0.04v2 = 0 Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. -1675 + 12.5v + v2 = 0 Move the constant term to the right: Add '1675' to each side of the equation. -1675 + 12.5v + 1675 + v2 = 0 + 1675 Reorder the terms: -1675 + 1675 + 12.5v + v2 = 0 + 1675 Combine like terms: -1675 + 1675 = 0 0 + 12.5v + v2 = 0 + 1675 12.5v + v2 = 0 + 1675 Combine like terms: 0 + 1675 = 1675 12.5v + v2 = 1675 The v term is 12.5v. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5v + 39.0625 + v2 = 1675 + 39.0625 Reorder the terms: 39.0625 + 12.5v + v2 = 1675 + 39.0625 Combine like terms: 1675 + 39.0625 = 1714.0625 39.0625 + 12.5v + v2 = 1714.0625 Factor a perfect square on the left side: (v + 6.25)(v + 6.25) = 1714.0625 Calculate the square root of the right side: 41.401237904 Break this problem into two subproblems by setting (v + 6.25) equal to 41.401237904 and -41.401237904.Subproblem 1
v + 6.25 = 41.401237904 Simplifying v + 6.25 = 41.401237904 Reorder the terms: 6.25 + v = 41.401237904 Solving 6.25 + v = 41.401237904 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + v = 41.401237904 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + v = 41.401237904 + -6.25 v = 41.401237904 + -6.25 Combine like terms: 41.401237904 + -6.25 = 35.151237904 v = 35.151237904 Simplifying v = 35.151237904Subproblem 2
v + 6.25 = -41.401237904 Simplifying v + 6.25 = -41.401237904 Reorder the terms: 6.25 + v = -41.401237904 Solving 6.25 + v = -41.401237904 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + v = -41.401237904 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + v = -41.401237904 + -6.25 v = -41.401237904 + -6.25 Combine like terms: -41.401237904 + -6.25 = -47.651237904 v = -47.651237904 Simplifying v = -47.651237904Solution
The solution to the problem is based on the solutions from the subproblems. v = {35.151237904, -47.651237904}
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